A lot of people are excited today not because the unemployment rate is low (it's very high -- 8.9 percent), nor because the economy is adding jobs (it lost another 539,000 last month, according to statistics just released by the BLS), but merely because it's losing jobs less quickly. That is, the second derivative of the employment rate -- the change in the rate of change -- has improved. This is what the situation looks like:
The economy started losing jobs in January, 2008 and has continued to lose them ever since. The peak month for job losses -- so far -- was January 2009, in which 741,000 jobs were lost. The month at which the second derivative bottomed out -- the time when the rate of job losses was increasing the fastest -- came in November.
The $787 billion question, of course, is whether a decrease in the rate of job losses indeed portends a recovery, or whether such data is subject to false starts. Let's take a somewhat high-level view of the progress of the employment situation over the previous five recessions.
First, the recession of 1973-1975. The red bars indicate, by the way, when we were "officially" in a recession, according to the NBER:
This was, at first, a "jobless recession", the primary concern instead being the extremely high inflation rates triggered by (among other things) the oil crisis. The economy, however, began shedding jobs with a vengence in November 1974, with job losses peaking at 602,000 in December 1974 -- a rate that would be equivalent to about 1 million job losses given today's population. By January, 1975, however, it already looked like the worst was over, with job losses decreasing to 360,000, and indeed the economy had officially pulled out the recession by April and was adding jobs again shortly thereafter. Here, then, improvement in the second derivative does appear to have had some predictive powers. Next up, the recession of 1980:
This was a short-lived and relatively orderly recession; an improvement in the second derivative in June 1980 was followed by the end of the recession two months later. It was, however, followed not long afterward by a much worse recession...
Ah, the good ol' recession of 1981-82, the one to which the present one is most frequently compared. And note the presence of not one, not two, but three false starts. In February 1982, job losses slowed all the way down to just 6,000 jobs, but things got worse -- not better -- in March and April. Then in May, job losses slowed to 45,000, before accelerating again throughout the summer. Finally in August, job losses slowed from 343,000 to 158,000 before increasing again in September and October. This is the sort of example that should make us very cautious.
Next, the early 1990s recession:
There is arguably a false start here in September 1990, when job losses slowed from 208,000 to 82,000, although the recession had barely even begun then. The job-loss situation also appeared to be getting a bit better in December, 1990, but the peak month for job losses in fact wouldn't come until two months later in February.
Finally, the recession of 2001:
We have to include a lot of data here because employment didn't bottom out until June 2003 -- some 19 months after the recession had officially ended! Although the main period of job losses, from the summer of 2001 through the spring in 2002, proceeded in a relatively orderly fashion, there were still places where we could have been deceived. For instance, the economy began adding jobs in June 2002, but then lost them again for the next three consecutive months; a similar story took place in January 2003.
In sum, employment rate data is fairly stochastic, and if there is ample reason for optimism (and I believe there is), there is also ample reason for skepticism.
5.08.2009
Hooray! The Second Derivative of the Unemployment Rate Improved!
@ 12:12 PM
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83 comments
It's not "Employement" but "Employment". Need a spellchecker?
The ragged finish to the recession of 2001 may have had to do with September 11. Not only did stocks plummet but a lot of businesses began to contract (i.e. shedding employees) out of sheer fearfulness over what lay ahead.
Very informative and enlightening. You guys never cease to impress me on this website. First thing I read every morning.
Excellent post Nate! I well remember the jobless recovery of the first George W Bush Recession! I was laid off during that resession as well and I have been frightened that this recession will play out the same. Thanks for showing that some Recessions are different. There does seem to be a pattern to the 2nd Derivative and when the unemployment starts to improve, except again for Bush's First Recession. I guess the question is whether that 2nd Derivative column will stay in the black or jump back into the red. But I agree a good sign for cautious hope!
Look at initial unemployment claims. It has a much better track record in identifying business cycle troughs.
http://www.econbrowser.com/archives/2009/05/this_shoot_is_d.html
The "2nd derivative" is not equal to the second finite difference listed in your tables. While the trends are equivalent and your arguments are valid, equating these two things is bad math!
So in short, another piece of evidence that the corner hasn't been turned but we're within [perilous] reach of it.
Funny how we've gone from "the greatest economic challenge in our lifetime/since the Great Depression" to "ample reason for optimism" in just a few short months with little more than a bloodied but recovering stock market, unemployment only at 9% (I realize that's high but far from double-digit, or even 20%+ like the GD), a moderate but brief drop in GDP, and very low inflation.
Either all of that fear-mongering from a few months ago was completely uncalled for or this is the biggest "false start" in modern economic history. Either way, somebody owes someone an explanation. Either there was rampant lying and distorting from this Administration early on to scare people and lay the foundation to push a radical agenda towards social democracy or we've got catastrophe still just in front of us.
You can't have it both ways! If we were truly f'ed, then we're still f'ed, and have plenty of f'ing left to go. Or Obama and Co. are the biggest liars since....well, since George W. Bush and Co.
Working America, of which I'm the online organizer, create a site to help people who are still in this mess. It's a one-stop guide that links workers to the resources in their area, from unemployment offices to veterans' services to child care. It also offers the opportunity to talk to others and share support and lessons learned.
Use it or share it, people still need it: http://www.unemploymentlifeline.com/
You mean that the first derivative has improved, and the second derivative is now positive, if I'm not mistaken.
Nate, do these job numbers include public sector jobs? If so, there is a big distortion in that a large number of government employees were hired to perform census work. Which might mean that the job loss rate in the private sector is at a higher rate than last month. Government jobs don’t produce economic growth.
Check it out.
Bill Warner
www.paladinandassociates.com
All this is an inflection point. It means that there is not a foot on the gas pedal and we are slowly decelerating. Not excellent but good.
Aaron's exactly right--the first derivative has improved, resulting in the second derivative being positive. And, as Brian said, what you tabulated was not the second derivative. Looking briefly at the tables, it seems like at least some of the "false starts" came in the month after an abnormally high job loss, while the "real" recoveries in the first derivative came after months that were more in line with the trend. If you actually plotted the data, this might be more apparent.
How can you have a second derivative for April when your data stops at the last point. Only a projection.
Once we get the next data point you can draw the tangent to the curve, and compare that to the last tangent.
I love the quantitative analysis but lets be clear. And how about some confidence intervals? Why stop half way?
Interesting analysis, and great article. Just want to point out, though, that a derivative and a finite difference, though similar in concept, are not quite the same thing.
Keep up the awesome work!
First derivative, not second, as others have noted. I'm struggling to maintain my faith in you.
This one feels rushed. Besides the derivative issues previously mentioned, you have rampant typos, not the least of which is "Horray" in the title. I think you meant Hooray (well, either a typo or you are using some cool slang that I didn't hear about yet... or are creating it!)
As always, though, a fun read!
Like what Aaron and Carl said. That's a pretty basic math literacy error! It's not a picky point like the 'finite difference' people are making, but an error of one (out of two) in the order of a derivative- the main point of your post.
The "function" is the number of jobs in the economy. The change in the number of jobs is the first derivative. The change in the change of the number of jobs is the second derivative. (Similalrly, the rate of inflation is the first derivative of the price level, the change in the rate of inflation is the second derviative and so on). To me, this is the natural interpretation and the one Nate intended. I can see that if you think of the function being the unemployment rate and not the level of employment being then it would be the first derivative, but snarkily posting as if that is the only way to think of it and implying that Nate's an idiot is rather unbecoming.
I agree with SReed, Nate is correctly using the phrase with the correct intended meaning. The point isn't just that the rate of job loss has improved, but that the second derivative of the number of jobs as a function of time has made positive gains statistically significant enough to be meaningful and newsworthy.
So, how bad does the economy have to be when losing only 537,000 payroll jobs is considered a "ray of hope"?
Just as some perspective, prior to the last 6 months, a job report showing 537,000 lost jobs would have been the 6th worst monthly showing since this record-keeping began in 1939. Thanks to the current recession, however, it's actually only the 6th worst showing in the past 6 months alone.
Looks like all those threats and mockery of Nate by The Mule Rider are wearing the poor boy down. His star is starting to fade, and he's getting really sloppy of late.
The quality of posts on this site has deteriorated rapidly over the last few months, and it's getting where both the qualitative and quantitative ones are either partisan-filled rants devoid of intellectual acumen or a gross misunderstanding of fundamental mathematical concepts. And typos are littered throughout each and every one as well. Nate has gone from outstanding to respectable to questionable to garbage in about the span of six or seven months. That's going from a meteoric rise to a humiliating fall.
"Ah, the good ol' recession of 1981-82, the one to which the present one is most frequently compared."Um a quibble. If anything, the 81-82 recession is the one to which this one is contrasted, not compared. 81-82 resulted from the Volcker Fed cranking up interest rates to squeeze out inflation. When they were satisfied that inflation was tamed, they dropped the rates and the economy soared back up to its latent employment level.
By contrast, this recession came after years of deliberately -- even obdurately -- low interest rate policy by Greenspan's Fed, the policy that drove the real-estate bubble. This time, with a recession resulting from the wreckage of that popping bubble, there is no possibility of recovering by lowering interest rates, since they're already at or near zero. That's the reason the Fed is nearly helpless this time around.
Not my arguments -- Krugman has been yelling himself hoarse on this very point.
For the complainers, there's nothing wrong mathematically with what Nate wrote. Jobs are being loss less quickly. In addition, the second derivative has improved. (It was negative before and now it is positive. So it improved.)
Moreover, anyone who has used calculus in the real world knows that a series of finite differences is often referred to as being a derivative.
No Brainer, recall that in the past 3.5 months, we've seen a $multi-trillion money supply expansion by the Fed, and a >$1 trillion fiscal expansion (stimulus plus new release of TARP funds, though only about 1/4 of it is actually out in the economy).
Do you really believe that neither of these has had any effect on the economy? Or perhaps you have no brain, as your pseudonym would indicate?
Just as a side observation -- the job creation record under George W. Bush was HORRIBLE. In each of those charts, the number of jobs seems to keep jumping by ten million or so between each recession - with a big jump of 22 million jobs under Clinton.
But then you see that George W. Bush started with a baseline of about 132.5 million jobs, and ended his presidency with 134.3 million jobs. Only 2 million new jobs in 8 years?!
In fact, there are fewer jobs (April 2009) now than when Bush took office in Jan. 2001!
That some conservative trickle down economic policy we can believe in, folks.
"For the complainers, there's nothing wrong mathematically with what Nate wrote."
Nope, in his many mentions of recovery prediction by improvements in the "second derivative", he points to times when the "second derivative" goes positive, ignoring times when it improved but stays negative. Similarly, when the second derivative declined but stayed positive, he did not count it as a decline. He's clearly talking about improvement in the first derivative, resulting in a positive second derivative.
And I use calculus in the real world, and have never heard of a series of finite differences being referred to as a derivative. One is proportional, the other absolute. This post needs to be corrected and improved. A rare miss.
If the rate of increase is decreasing, then the instantaneous value of the second derivative is a negative number. This is a point of inflection. I think Nate's use of this is correct...A negative number in this case indicates a better condition than a positive number in terms of the trend.
I also believe the headline of this post is meant to be tongue in cheek...
And also....lighten up on spelling and grammar. This is not English class, these are not assignments, and you are not the teacher. You look old and pathetic when point these out.
Yes, as mentioned above, the Census Bureau hired 66,000 workers in April. That only happens every ten years or so.
Also, see http://www.shadowstats.com/article/employment
Fair enough point about the census workers, but the Shadowstats site....uggh. So full of nonsense it's hard to know where to start. Anyone smart enough to be at 538 ought not to be putting any faith in John Williams.
Wow. No one told me it is pick on Nate day.
Since I do not have a math degree, in fact I took Calculus for Humanities in college and remember little or nothing and I don't consider myself the grammar police despite a stint as an English 100 tutor in college, I guess I will just have to pick on Nate's glasses.
It never ceases to amaze me how often people comment to complain about typos. If they bother you so much, don't read the blog. (I am excluding Pragmatus because usually he comments on content and not typos or grammar except for the past few days. Is May National Grammar Month?)
Even if you factor out the 66k jobs (according to a previous post) created by the Census Bureau, that leaves a 'Second Derivative' of over 90k, which is still easily makes April the best month since the start of the recession in terms of that measure.
Either there was rampant lying and distorting from this Administration early on to scare people and lay the foundation to push a radical agenda towards social democracy or we've got catastrophe still just in front of us.
You can't have it both ways! If we were truly f'ed, then we're still f'ed, and have plenty of f'ing left to go. Or Obama and Co. are the biggest liars since....well, since George W. Bush and Co.,
Wow, what a dick. "Radical agenda"? What, like EFCA not getting passed, or Max Bauchus not giving single payer healthcare advocates a seat at the table and having healthcare professionals arrested at hearings? Hardly social democracy.
As for lying and distorting to scare the American people. Are the people out of work lying? Are the likes of Paul Krugman and Nouriel Roubini lying? Maybe President Obama and his team have been working day and night to avert economic disaster. That's why America is in a severe recession, instead of a full-blown depression. Here's hoping the American and World economies are fucked for years to come, So we'll know Obama wasn't lying, eh?
You're not one of those Ron Paul nuts, are ya?
For the people complaining about derivative vs. finite differences:
In several math and stochastics courses I have seen the finite difference s(t+1)-s(t) referred to as the "discrete derivative" (with analogous definitions for the second derivative, and so on).
For those complaining... Assuming unemployment is a continuous doubly differentiable function, then at some point in March or April d^2J/dt^2 was 160,000 jobs/month^2.
Admittedly that's not the second derivative for all of April, and perhaps not for any point in April, but...Does it really matter? What would you prefer to call it? "Change in change in jobs?" While more accurate, that's a bit too word for my tastes. Delta delta jobs? Delta^2 jobs?
Jen...
Well, one can just as easily find it weird that someone would use a post, such as you did, to complain about others' complaints. Seems to me both are bumps on the same log.
For some people, spelling and grammar are an important part of any presentation. For others they are less so. Both attitudes, it seems to me, are valid.
If you were trying to instruct people to "ignore the grammar and spelling mistakes" I can just as easily, and with equal justification, say to you "ignore those posters who assign more importance to grammar and spelling than you do".
Nobody is picking on Nate. Yesterday I made a glaring mistake (using it's instead of its) and I was perfectly content to be openly called on it.
Do you have any thoughts about the content of Nate's post?
Change in GDP, a common measure of the economy, is also a 2nd derivative, of total wealth. Whether or not GDP is high is seen as less important than how it's changed.
Carl said...
Looks like all those threats and mockery of Nate by The Mule Rider are wearing the poor boy down. His star is starting to fade, and he's getting really sloppy of late. I take it since you are also "No Brainer", in a brand new account, that you in truth the same fellow with new sockpuppets? Slow day, Donnie? LOL
Do you have any thoughts about the content of Nate's post?Not really. Most of the time I enjoy reading other commenters discuss the post, including you, particularly when it is something I don't have a whole lot of knowledge regarding, like economics.
What I did think was it was a good post comparing prior recessions to the current one, and that yes we may be "turning the corner", but there may be another corner and another corner just ahead. I will say the recession at the end of Bush I's term seemed much worse to me than the numbers Nate provided indicated. I found that interesting. I guess it was because that was the first recession when I was an adult, though I was still in college so I just perceived it as really bad.
Truthfully, I have become used to a typo or grammatical error here and there not just on Nate's site, but everywhere. I guess I have just learned to be accepting, because I make mistakes too, including the dreaded "its" vs "it's" or the wrong flavor of there/their/they're which is my personal bugaboo.
Slow day, Donnie? LOLFunny thing is, if you think Donnie is my real name, you couldn't be further from the truth.
Funnier thing is that every ounce of poison and venom I hurl at Nate is most deserved and is very representative of the truth. He is a laughingstock and the joke is on blind followers such as yourself.
So go "LOL" yourself back to the mental ward.
This is one of the most distressing posts I've seen here. As others have said, this is basic math literacy. If the function is the number of jobs, then the first derivative is the rate of change in the number of jobs. That rate of change has improved, going from a large negative number to a smaller negative number--i.e., the graph of the function has gone from a steep downward slope to a less steep one--so the first derivative has indeed increased. (Of course, the second derivative has increased also, from a negative value to a positive value.)
You are right Carl, Nate is such a luaghingstock he is on Time's list of 100 Most Influential People. I am sure you are just upset because he assed you out since you were #101.
Why would you bother hurling poison and venom at anyone? Has Nate done you a particular wrong? Why is it worth your time?
re: "Government jobs don’t produce economic growth." from Bill's much earlier post.
I know this statement is now taken as received wisdom from academics of the Friedman school, but can anyone tell me - What IS the evidence or even the argument for this assertion?
The counter-argument, which I find persuasive, is simple.
- Someone does a job (necessary or not) for which they receive wages
- Those wages get spent in the private sector (yes... a portion goes back in taxes) for goods and services.
- The creation of those goods and services require labor that receives wages (and form a capital base to fund future economic growth).
- And so it continues through some "multiplier" (I've heard estimates of 5 to 9 multiples, but, however large or small it may be, there is some multiplier).
In what way can this "thread" of transactions not result in "economic growth"?
NOTE: If it happens the government work people were being paid to do was an "intrastructure project" (formerly called "public works") that work created new public capital that is now available for the use of private business at no additional cost.
Being rich during a recession can almost be as bad as being poor. The only difference is that the rich have more to lose. RealtyTrak, a research firm that follows mortgage trends, recently reported that the foreclosure rate on homes valued at more than $729,750, also known as the jumbo-mortgage limit, rose 127% in the first ten weeks of this year compared to the same period a year ago.
Bloomberg reports that about $500 billion of prime-jumbo mortgages are bundled into bonds. The default rate on those bonds may rise as high as 10%, leaving banks with yet another set of substantial write-offs.
The losses from the bonds held by banks may be covered by the TARP capital they have received from the government or the money that they have been asked to raise as a result of the “stress test” process. That leaves the more important issue of what it means when the financial distress of the wealthy and nearly wealthy begins to look like the money problems of everyone else.
The country counts on the rich for a large portion of it tax receipts. The new budget assumes that upper income households will pay an even larger part of their earnings each year from now on.
The fact the rich are now losing their homes is a signal that the real estate market has further to fall and that the projections for receipts to the IRS from individual taxpayers used to create the assumptions for the budget are wrong.
No one working on forecasts about the activity of home sales and home prices has any illusions about the severe problems at the low and middle segments of the market. Real wages are not rising and unemployment may reach 10% this year.
Most of the people out of work will be those who earned between $25,000 and $75,000 a year, not the rich. Most homeowners are just that -- regular middle class workers.
People living on relatively fixed incomes usually do not have the resources to cover their daily expenses for a long time if they lose their jobs or suffer a drop in their earnings. The one thing of value that they had, their home, may currently be worth less than it was 20 or 30 years ago.
The wealthy, at least, have opportunities to make money beyond their salaries, whether it is by holding stocks, owning a private business, or being paid a performance bonus. That has probably allowed those people with high incomes who are defaulting on mortgages for expensive homes the reserves to make mortgage payments for a few additional months, if they are defaulting because they are out of work.
The new foreclosure data show that many high-end homeowners are running out of resources for keeping their homes. That means the portion of the home market with the most expensive houses is beginning to collapse. If it follows the pattern of the rest of the sector, prices will correct downward quickly and brutally. The housing crisis will have moved to upper-tier properties, which will push down overall home prices even more.
Banks will take back more foreclosed houses. Those that they seize this time will just be larger and more opulent.
The tax consequences of these problems at the top of the housing market cannot be underestimated. Congress and the Administration have decided to push more of the tax burden to the high end of the income brackets. Whether this is morally or economically defensible won’t matter much if the total tax dollars from people making over $250,000 a year is well below budget. Even if the federal government has a perfect track record of holding to its expense plan for the next two years, IRS receipts could be off by tens of billions of dollars.
Local tax authorities that rely on property taxes to cover most of their needs will probably have more trouble than the federal government. In many municipalities, property taxes are the primary source of revenue for schools and local services. Rising foreclosure rates on the most valuable homes will eviscerate local tax bases. The municipalities will only have one place to turn ultimately and that is to the federal government.
As the rich become poor, the federal budget will fall apart.
Since the data is "stochastic" as Nate puts it, we should perhaps smooth it (e.g. moving averages) to get a better picture of the changes in sign of 2nd derivative, i.e. the points of inflection.
Nut Butter...
I disagree. The poor, particularly those living from hand to mouth, suffer intensely from even the slightest downturn in their income. While the rich may lose more in terms of dollars, they rarely get thrown out on the street or have to give up buying medicine in order to put food on the table.
How many rich people become homeless in a recession, even this one? You could probably count them on one hand. Someone who just lost a million-dollar home is not going from that experience to a soup kitchen. If they had the resources to buy a home that expensive, they have resources and fallback-options the poor can’t even dream of.
I think the problem is focusing on dollars lost rather than erosion in one’s standard of living. A rich person getting cut down a peg or two bears no relation to the truly down-and-out undergoing the same thing.
Guys, I really don't see why you think the term "Second derivative" is wrong.
f(x)= the number of jobs
f'(x)= number of jobs gained/lost since the month before
f''(x)= difference in the number of jobs lost between last month and that month.
And it's the second derivative.
In any case, news from Canada: the number of jobs here grew in the month of April by 38,000, which is within the margin of error, but still. Unemployment rate (at 8%) didn't change because of population growth.
Since we've already assumed that employment is a continuous, twice differentiable function, let's go ahead and say that it can also be represented as a Fourier series sum_over_i(a_i*sin(2pi*i*t). Each of the terms in the sum is periodic. The first derivative of each term will be cos, and will lead by pi/2 radians. The second will be -sin, and will lead by pi radians. So the second derivative leads the function by half a cycle. So if we want to know when employment reaches baseline again, we just compute cycle length by weighting all the coefficients in the fourier series, and then divide by 2. N.B.: the above mathematical reasoning probably causes economic meltdowns.
Jeff Redmond...Assuming no deficit spending, the argument is that a private sector worker would have spent that money on goods, but instead he is taxed to pay for the govt worker's salary. So the govt worker's consumption is not 'extra'. It is simply shifted, via taxes, from the private worker. So it should have a zero net impact on GDP, but on top of that, you get losses from the inefficiency of the govt.
The argument with deficit spending, is that you are attempting to time-shift future GDP to the present, but that a rational worker would choose to save rather than spend in the present because he anticipates the taxes in the future, thus nullifying the time-shift. Plus you lose money paying interest on the treasury bonds.
do the same math for foreclosures, please.
On derivatives:
There's been some confusion. Yes f" has improved. That's not the news. The news is that f">0, i.e. that it's good, not just improved. It's f' that's still bad (<0) but is improved. Good f" and improved f' mean the same thing.
It's embarrassing to even have to point out this sort of thing. I'm sure it was just a slip on Nate's part, but the comments seem not to be kidding.
Is it really possible that this nominally quant site is not functioning at high school level?
@Dave:
Your argument is a great rebuttal of deficit spending via tax cuts. You are arguing that a rational worker will save his or her tax cut in anticipation of higher future taxes.
If deficit spending is generated via creating new jobs, that will cause an increase in demand by increasing employment. It will also result in new revenues to the government from people in those new jobs, and by the effects of increased demand. I'm not claiming that such deficit spending will pay for itself, but that there is feedback that partially compensates for deficit spending when new jobs generate increased demand.
Not a comment on Nate's post.
Not a comment of anyone's spelling, grammar, or usage of words, etc.
Just an observation on some of the posters:
Blogger profile for 'No Brainer' is:
http://www.blogger.com/profile/09121249774640851066
"Profile not Available"
Blogger profile for 'Carl' is:
http://www.blogger.com/profile/09121249774640851066
"Profile not Available"
Blogger profile for 'Nut Butter' is:
http://www.blogger.com/profile/09121249774640851066
"Profile not Available"
Do I detect a pattern here?
Mike in Maryland
My Blogger ID is http://www.blogger.com/profile/02848893412251095965
Jen gets best post o' the day award, for this:
"You are right Carl, Nate is such a laughingstock he is on Time's list of 100 Most Influential People. I am sure you are just upset because he assed you out since you were #101."
☺
Mike in Maryland...
I didn't even know there was a profile I could edit. Learn something every day...
Do I detect a pattern here?
The I tried my best to beat the system but the system put me back in my place They maintained a delicate balance where no one got in nobody's face commenter is in the building.
All of you people bashing Nate's calculus might want to do a little brushing up yourselves.
Divide the difference in the employment numbers by 1 month (the time interval between data points) and you get a change per unit time. Or the average derivative of the employment over that month. Divide the difference in the change column by the 1 month interval and you get the average 2nd derivative.
Of course the numbers are not the exact derivatives at specific points (although by the mean value theorem, they must be the derivative at some point during the month). They are obviously average derivatives for the month-long intervals.
People who know something about math and are being pedantic about the difference between "second derivative" and "second difference" look a bit silly to those of us with even more of an education in math.
Until statistics are continuously updated, and not just at regular intervals, we will not have access to actual second derivatives. And yet time is a continuous phenomenon, so it is more than reasonable to refer to time-dependent variables using the continuous language of differential calculus.
Nate is using difference equation data to make a point about continuous-time variables. Get it?
People who are pedantic and wrong are really tiresome.
Prag,
If you haven't found it yet, left click on your user ID in any of your posts to open the profile in a new tab or new window. Then click on the 'Edit Profile' button and make any and all changes you wish to make.
You CAN change your profile name, but the Blogger ID remains the same.
Mike in Maryland
My Blogger ID is http://www.blogger.com/profile/02848893412251095965
Mike in Maryland- good catch. I will keep my eye out for blogger ID's that end in 1066.
Pragmatus- thanks for correcting my typo on laughingstock and not pointing it out! :)
Prag,
Correction - right click, not left.
I can be somewhat dyslexic at times when it comes to left/right when giving directions!! VBG
Mike in Maryland
My Blogger ID is http://www.blogger.com/profile/02848893412251095965
@Mike in Maryland
I say, I say that kid is about about as sharp as a pound of wet leather. What a schnook. ;)
Carl/No Brainer [/Smoking Aces/Donald/etc, etc] the sock puppet, that is.
To the other math weenies complaining about the finite difference, c'mon give Nate a break. OF COURSE he meant in the limit of the interval shrinking to zero. :)
I once sat through an econ lecture where the prof kept talking about rate of change as the measurement is taken over smaller and smaller intervals. At one point I almost broke and stood up to shout "It's a derivative! For god's sake just say derivative, our heads won't explode!."
Can't anybody here spell?
No one noticed that the very first word in the title of this post is misspelled?
It's "hurray",Nate,not "horray."
"it's losing jobs less quickly. That is, the second derivative of the employment rate -- the change in the rate of change -- has improved."
Actually, that means the FIRST derivative has improved (becoming less negative). The information we know about the second derivative given the quoted statement is not that it has improved, but that it has a positive value. It doesn't have to "improve" further, as just holding at its current value will make the unemployment go down eventually.
whispers said...
"People who know something about math and are being pedantic about the difference between "second derivative" and "second difference" look a bit silly to those of us with even more of an education in math.
Until statistics are continuously updated, and not just at regular intervals, we will not have access to actual second derivatives. And yet time is a continuous phenomenon, so it is more than reasonable to refer to time-dependent variables using the continuous language of differential calculus.
Nate is using difference equation data to make a point about continuous-time variables. Get it?
People who are pedantic and wrong are really tiresome."
I just have to do this.
1. Time isn't continuous, according to physics. A time of length < 10^-42 or so doesn't have any physical meaning (look up Plank time for this), thus time is really discrete. And slightly less pedantically,
2. Employment (or unemployment) is also a discrete quantity, which means a true second derivative would be zero (no change) or infinity (someone just lost/gained a job, or a fraction thereof). BTW, this also means the intermediate theorem can't be used.
But, I would also hope that everyone would understand what Nate was getting at.
People who incorrectly criticize people who are pedantic and wrong are really tiresome. :)
(Now queue someone else to show why what I said wasn't correct either...)
Christ. is that the best you can do? Using quantum physics to refute someone's claim that time is continuous in economic theory?
And spelling "Planck" wrong while you're at it... ;
While it's true that much of current US employment being created consists of government jobs (Census or otherwise), it's been this way for at least a quarter century now, and is nothing new.
When the US began losing manufacturing jobs in earnest, we replaced them with tech jobs, those in the professions, various low-level service jobs (such as waitressing and bartending), and more government jobs. When the US began losing tech jobs as well, we replaced them with more low-level service jobs, and even more government jobs.
So for quite a while now, three areas of the economy have seen consistent job growth (not counting bubbles such as in construction which was powered by housing): the professions, low-paying service jobs, and government jobs. Practically the only goods of physical value where the US is now a net producer are certain natural resources.
This creates a bit of a donut hole. Those well off enough to enter the professions or similar high-end service sector jobs have been doing fine. Those at the bottom end may not have been doing that well, but there have at least been a glut of low entry jobs that have kept unemployment lower than it otherwise would have been. What of those in between? Basically the only growing group of middle class jobs that offer benefits and upward mobility is government jobs, which I, as a moderate liberal, see as potentially dangerous. It's one thing for government to provide a minimal safety net, but government as primary employer is a situation we probably want to avoid.
The problem for right-wingers and neoliberals, of course, is that the only way to curtail government jobs is to bring back the types of jobs where the worker has power and private sector unionization will probably re-establish itself. They'd much rather not, and just keep the US an economy of bartenders and hairdressers. The political problem with this is that this tends to produce a rather miserable, static economy.
The choices are thus (1) to allow back lucrative private sector jobs that will re-create the economic dynamics of the 60's and 70's in a hurry, or (2) continue to hollow out US employment, keep the economy on a tightrope, and let government employment flourish. Whatever they may claim, they probably prefer (2), as they themselves won't be hurt for the most part, and any long term damage can simply be looped back and blamed on the government. What they really want is for workers who'll provide the productivity of a technology-based private sector industry, but with the malleability and bargaining position of most workers in low level service sector jobs today. A fundamentally 19th century dynamic, in other words.
For various reasons (i.e. progress), the 19th century is never coming back. Any futile attempt along these lines will probably end up devastating the US in time for (3) socialist Europe and communist China to win.
How a prolonged recession would affect all this is unclear. On the one hand, strong economic shocks have often been used to force through right-wing economic programs that would otherwise have no chance of passing. On the other, that doesn't seem to be the prevailing mood these days, and American democracy is much shrewder and better developed than the third world countries where that's happened. Much of the economic movement since Reagan has only been possible because the deterioration of average living standards has been gradual and under the surface. Will this recession lay it bare? Possibly, but only if it's sharp enough, which means it's not worth it. The political tide has already turned, anyway.
@Mike in Maryland.
Haha, great work. To Carl/No Brainer/whatever other sock puppet ID's you're cowardly hiding behind: I don't know much about Nate, except that since the election he's become an online superstar and a rising media figure. The only laughingstock here is you, who even before being exposed as a dishonest sockpuppet, pathetically believed that a beloved fellow right wing troll accomplished anything on this forum besides embarrassing himself.
The next time someone claims to have "once been a fan of this site, but..." I'll be sure to check the Blogger ID.
Let's get away from math taxonomy debate - it's hard to see a public debate about second derivatives as a sign of cultural decline. (I think the correct term is a second difference function, from discrete math, but really who cares?)
A bigger issue for this post is that employment figures are noisy. If the weather's nice in January, fewer people are hired to remove snow, or more substantively, as noted in one of the posts above, 9-11 caused firms to cut jobs.
Differencing magnifies the size of these shocks relative to the signal provided, which may account for some of the "false starts" that appear in the data. One way to deal with this is to take a three-month moving average of the final series, since the shocks then tend to average out. I think this series would be more helpful in diagnosing inflection points.
Lewis
FYI.
That post on the recession-induced problems of the rich originated here.
Our correspondent in Memphis has previously posted comments consisting entirely of an essay having to do with economics that originated elsewhere (without attribution or link) using other IDs and names.
Erm... as I understand it, in terms of differentiation of an equation, the first derivative (dy/dx) is the gradient, or 'how quickly you're losing jobs'. The second derivate (d^2y/dx^2) is 'how fast is the rate of change changing?' Nate is therefore more or less correct, and so the worsening of the situation is not as bad as it was (if that makes any sense at all), although of course, he's using the wrong terminology.
Of course, once the recession has ended we'll have the fun and games involved in reducing the Federal deficit and paying off all that nice debt we incurred saving the banks.
scangst: some looked a scangst at Nate Silver's use of the second derivative
If the inflection point continues to improve through the summer, then their will be cause for optimism.
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Ass Rider's stench is the same no matter what his handle is.
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This discussion shows how a small amount of math knowledge is a dangerous thing.
All of the grammar Nazis can get bent too.
Today's Flight From Reality Journalism...
Of all who read yesterday’s unemployment figures only Fox News thinks the rate is still rising…
I have maintained a very healthy skepticism about all the "green shoots" being reported about the economy in recent months. It seems a lot of this is "down so far it feels like up," because the months of August-September were so disastrous, both for GDP and employment.
It's like all the positivity about the recent "bull(sh*t) market" that has seen a 35% increase in 2 months...while conveniently leaving out that it's still down 30% from 1 year ago. People are still overindebted without real wage growth (check the stats on the large number of people forced to work part-time instead of full-time), and until that starts to change over, this recovery is cosmetic only.
And we're not even bringing up the huge amount of cutbacks and layoffs that will be happening in the public sector in the next 6 months. Wait till those show up in the stats and reverse the recent gains in government payrolls.
Now imagine imagine if Gramps and Mooseburger were trying to solve this. Thank God this country chose wisely last November.
"Horray! The Second Derivative of the Unemployment Rate Improved!"
Second derivative? Huh? Nate don't you know Physics from Calculus? The "Unemployment Rate" is a term of velocity. The rate of change in the "Unemployment Rate" is a term of acceleration.
In proper English your headline should have read: "Hurray! The Acceleration of the Unemployment Rate Finally Decreased!"
Prag-
The terminology Fox News is using is,unfortunately,correct.The unemployment rate did increase.It was the job loss rate that decreased.Big difference.
I haven't posted in a long time here, mostly because of my lack of expertise, but since this is largely about mathematics, something I understand, I thought I'd chime in with my opinion.
The second derivative is technically the rate of change of the rate of change, and can only be computed using continuous functions. Hence Nate is "wrong." But some posters here have claimed that this term is used for the second discrete derivative, not something I've heard about. Nonetheless, I don't blame Nate for using this term, since I instantly understood what he meant. The purpose of his posts is communication, and since he successfully communicated, no fault lies with this minor misuse of language. It's better than saying the "change of the change," in my opinion.
However, I think the title should be something like "hooray, the second derivative is good!" Positive is good. To clarify, if there are enough jobs for everyone, that's saying the zeroth derivative of jobs is good. If there aren't enough jobs for everyone, but there are more jobs than there used to be, then you can say the number of jobs has improved, or you can say that the first derivative is good. What we have instead is a situation where the first derivative has improved, or the second derivative is good.
Although my work is more likely to involve actual derivatives than differences, I will comment that it is difficult to extract accurate derivatives from noisy data. In this case, there may be many short-term fluctuations that cause small changes in employment. By taking differences, and differences of differences, one is likely to see spurious fluctuations in the second derivative that are virtually meaningless. This may be the reason there have historically been so many "false starts." For this reason, it is HIGHLY adivsable to do SOME sort of smoothing before trying to draw conclusions. A single blip by this arbitrary measure is hard to interpret as anything.
WV - groph - we are trying to groph every smidgen of good news from this economic data.
Boing said...
Christ. is that the best you can do? Using quantum physics to refute someone's claim that time is continuous in economic theory?
And spelling "Planck" wrong while you're at it... ;
Knew I'd leave something for someone to pedantically correct my pedantic correction of someone's pedantic ... well, you see where this is going :)
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