Where do businesses find people to hire? A few new employees – graduating students,
for example – are recruited from outside the labor force, but I’m going to
ignore them (as later I will also ignore retirees, figuring that they roughly
offset each other). Most new employees
come either from among the unemployed or from other firms. Hiring the unemployed is easy inasmuch as
they’re usually knocking at your door asking for jobs. On the other hand, the selection process
might be difficult, since they aren’t doing a job now, so you have to make an
educated guess as to whether they’ll be good at the job for which you’re
hiring. Hiring people from other firms is
difficult in that you have to go out and actively recruit them, as well making
an offer that justifies leaving their old job, but the selection process is
easier, because all you have to do is find someone who is already doing a job
similar to the one for which you’re hiring.

So there is a tradeoff.
Presumably the terms of this tradeoff depend on how many people are
unemployed: if only a few people are
unemployed, then the number of qualified unemployed applicants will be low, and
they’ll be in demand from other firms, so you’ll have to pay them well, so you
might as well just try to poach someone directly from another firm; if a lot of
people are unemployed, the number of qualified unemployed applicants will be
high, and they’ll be willing to accept less attractive offers, so poaching
might not be worth it. So here’s the
crux of my model: the fraction of new
hires that comes from the unemployed depends on how many unemployed there
are. Using “H” for total hires, “He” for “hires out of employment,” and “Hu” for “hires out of unemployment,” we have
Hu/H=f(U), where f() is some increasing function, and for adding-up, we have
H=He+Hu.

Now, why do people quit their jobs? Some retire, but I’ve already said I’m going
to ignore them. Some quit for other
personal reasons, and I’m going to ignore them too. A few people quit, especially when the labor
market is strong, because they don’t like their job and figure it will be easy
enough to find a new one. I’m also going
to ignore them. Most people who quit, I
believe, quit because they already have another job lined up. In other words, if we ignore all the
categories I’m ignoring, then the number of quits equals the total number of
new hires minus the number of new hires that are hired out of unemployment, or
Q=H-Hu. Putting this proposition
together with the one at the end of the last paragraph and solving
simultaneously, we get Q=H*(1-f(U)).

OK, what about layoffs?
It may sound crazy at first, but I’m essentially going to ignore
layoffs. I’m going to assume that they
happen at a constant rate. We do know
that layoffs tend to spike during the early part of a recession (or in the case
of the recent recession, in the middle, when the “Great Recession” took over
from the “little recession” that was already in progress). But the typical spike is fairly small
compared to the total number of layoffs.
(We notice those layoffs more because they result in significant spells
of unemployment, whereas non-recession layoffs often result in just changing
jobs, or in brief spells of unemployment that often aren’t long enough to
justify filing an unemployment claim.)
So the “constant layoffs” assumption isn’t too far from the truth. Also, layoff spikes are clearly
“disequilibrium” phenomena that induce changes in the unemployment rate rather
than explaining how a given unemployment rate is maintained. In thinking about the Beveridge curve, I’m
interested in the equilibrium relationship between unemployment and job openings.

And here’s the equilibrium condition. I’ll ignore longer run changes in the labor
force and the capital stock and define equilibrium as constant total employment
(which implies constant total unemployment, since I’m ignoring labor force
changes). Constant employment implies
that hires equal separations. I’ll
ignore “other separations” and assume all the separations are either quits or
layoffs. Then we have H=Q+L (where L
stands for “layoffs,” not “labor”).

Since I’ve assumed that layoffs are constant, we have three
variables here, U, H, and Q. We’re more
interested in hires than quits, so we can solve to eliminate Q, and we get H=L
/f(U). Since f() is an increasing
function, this gives as an inverse equilibrium relationship between hires and
unemployment.

Ultimately we want to relate unemployment to job openings,
since that’s what the Beveridge curve is about.
How do hires relate to job openings?
One traditional approach is to fit a “matching function” in which hires
are an increasing function of both job openings and unemployment. The theory is that it should be easier to
fill job openings when there are a lot of unemployed people looking for
jobs. I tried fitting such a function
using JOLTS data, and the coefficient on unemployment consistently came out
with the wrong sign, no matter how many polynomial time trends or dummy
variables I put in, and even when I included an interaction term between
unemployment and the availability of extended unemployment benefits. Actually, that result is what motivated this
model. While obviously a high
unemployment rate will reduce the number of people who quit their jobs in order
to fill job openings, it does not apparently result in those openings being
filled any more quickly. So my matching
function is a one-variable function. H=m(V), where V (“vacancies”) is the
number of job openings.

Empirically, I fit H=m(V) as H=a*V^b, where a and b are
fitted constants. (Why do I use that
form? Tradition, I suppose: it just
seemed reasonable. It allows for the
intuitive special case where b=1, so that job openings fill at a constant rate,
but one casual look at the data will tell you that b<1 in reality: openings
fill more quickly when there are fewer of them.) The fit is pretty good (“log V” explains 78%
of the variance in “log H” with a slope coefficient of about 0.5, implying that
H is proportional to the square root of V), but there is an obvious pattern in
the residuals. (The Durbin-Watson
statistic is a mere 0.7 – in case this post isn’t wonkish enough already.) The cumulative sum of the residuals peaks in
July 2006, suggesting that there may be a structural break in August. A casual look at the residuals strongly
suggests another structural break in July 2010.
Both purported structural breaks go in the same direction: a decline in the number of hires associated
with any given number of job openings.
So, contrary to what I said in 2010, it does
look like we are seeing more structural unemployment now than in the past. (In my defense, the first break occurs long
before the recession, so I was right to assert that recession had not produced
an increase in structural unemployment; and the second break occurs just when I
was making that assertion, so I had no data from after the break.)

After I had done all this pseudo-theorizing, I decided to do
a little pseudo-test of my pseudo-model, and it actually holds up surprisingly
well (allowing the function f(U) to have the same form as m(V), because don’t
all functions have that form, damn it!).
There is a nice, linear-looking, downward-sloping relationship between
the log of hires and the log of unemployment.
Log unemployment explains almost 90% of the variance in log hires, with
a slope coefficient of -0.37, and the coefficients are robust to the inclusion
of an ARMA(1,1) residual process that results in a Durbin-Watson statistic of
precisely 2.0. (Ooooh, talk nerdy to me,
Baby!) There is no obvious pattern in
the residuals. Surprisingly, there are
only 3 significant outliers (March 2003, November 2008, and May 2010; call them
“Iraq War,” “Post-Lehman,” and “Census”).
At least I find that surprising, because this is an equilibrium model of
a system that obviously, in real life, is subject to shocks that move it out of
equilibrium – as we know from the fact that the unemployment rate changes a
lot. If you take this test at face
value, it suggests that the equilibrating forces (which I haven’t tried to
model) are very strong.

So what does all this imply about the natural rate of
unemployment? To answer that question we
need a model of aggregate supply, and I happen to have one up my sleeve. Here’s my model: there’s a constant natural rate of job
openings. That’s it. If firms have an unusually large number of
positions to fill, they bid up wages, and you get accelerating inflation. If firms have an unusually small number of
positions to fill (like right now, but even more like three years ago), they
start to let wages erode, and you get decelerating inflation (although research
now suggests that it’s very difficult to erode wages that already aren’t
rising, so this won’t work very well unless there is some substantial inflation
or productivity growth to begin with – but all that belongs in another
post). Somewhere there’s a happy medium
rate of job openings, such that wages tend to continue rising at a rate
consistent with the expected rate of inflation.
That’s the natural rate of jobs openings. Or the Non-Accelerating Inflation Rate of Job
Openings (NAIRJO). Or the Non-Accelerating
Inflation Rate of Vacancies (NAIRV).

If the relationship between hiring and unemployment is
stable, as it appears to be, then my model implies that shifts in the matching
function will determine a shifting relationship between the (assumed constant)
NAIRV and the NAIRU (Non-Accelerating Inflation Rate of Unemployment, a.k.a.
the natural rate of unemployment). For
what it’s worth, my estimates suggest that the hypothesized August 2006 and
July 2010 shifts in the matching function would, collectively, increase the NAIRU
by a factor of about one and a third. So
if the NAIRU was 4.5% (my best guess, which happens to be conveniently
divisible by 3) in July 2006, it is 6% now.
Of course, by the time the unemployment rate gets down to 6%, there’s a
good chance that the matching function will have shifted again, but as for
which direction and how far, your guess is as good as mine.

UPDATE: Posted scatter of log hires vs log unemployment on Twitter.

UPDATE2: Posted graph of series hires/sqrt(openings) on Twitter.

UPDATE2: Posted graph of series hires/sqrt(openings) on Twitter.

DISCLOSURE: Through my investment
and management role in a Treasury directional pooled investment vehicle and
through my role as Chief Economist at Atlantic Asset Management, which
generally manages fixed income portfolios for its clients, I have direct or
indirect interests in various fixed income instruments, which may be impacted
by the issues discussed herein. The views expressed herein are entirely my own
opinions and may not represent the views of Atlantic Asset Management. This
article should not be construed as investment advice, and is not an offer to
participate in any investment strategy or product.