Business Employment Dynamics: Where Jobs Losses and Gains Come From

Below, Corrections graphically depicts transformed Business Employment Dynamics data.  The two data series are the proportion of gross job losses generated by closing establishments, rather than contracting establishments (click to enlarge).  Similarly for gross job gains generated by opening establishments, rather than expanding establishments.

Three things seem to jump out of the figure:

• Generally, around 20% of gross job gains and losses come from opening and closing establishments.
• Compared to the proportion of gross job losses that come from closings, generally a higher proportion of gross job gains come from openings.
• There has been a secular downward trend in the impact of closings and openings on employment.

The last point is probably bad news for the U.S. economy.

Business Employment Dynamics: 1992:Q3-2011:Q2

Below, Corrections shows Business Employment Dynamics data from 1992:Q3-2011:Q2.  We index to 1992:Q3=1, from data originally in levels.

• Gross job gains are the total people hired in a quarter (not subtracting losses).  U.S. generally has around 7.6 million total gains in a given quarter.  
• Expansions are businesses that reported more jobs than last quarter.  U.S. generally has around 6.1 million firm expansions in a given quarter.
• Openings are businesses that did not exist in the previous quarter.  U.S. generally has around 1.6 million firm openings in a given quarter.
• Gross job losses are the total separations in a quarter (not adding gains).  U.S. generally has around 7.4 million total losses in a given quarter.
• Contractions are businesses that reported fewer jobs than last quarter.  U.S. generally has around 6.0 million firm contractions in a given quarter.
• Closings are businesses that reported last quarter but are no longer active.  U.S. generally has around 1.5 million closings in a given quarter.

We generally think of having both gross job gains and gross job losses high as creative destruction:  while not much is moving, there's a lot of churn in the economy, generally very good.  We generally think of having both gross job gains and gross job losses low as stagnation or sclerosis:  not much is flowing in the economy.

The 1990's and the Great Recession both show prominently in the figure of BED data, depicted graphically below (click to enlarge).

Unemployment Flows from Labor Force

Below, Corrections displays the four places the unemployed go, from month to month (click to enlarge). They either find employment, stay unemployed, leave the labor force, or "other" (a very, very tiny category that would include dying, or immigrating, for instance).

June 2011 JOLTS Release: April 2011's Beveridge Curve

Using the recent unemployment rate from the CPS and yesterday's JOLTS release, Corrections offers an updated Beveridge curve (click to enlarge).  Note the adjusted axes, so that recent trends can be seen more easily.

May 2011 JOLTS Release: March 2011's Beveridge Curve

Using the recent unemployment rate from the CPS and yesterday's JOLTS release, Corrections offers an updated Beveridge curve.

May 2011 JOLTS Release: March 2011's Beveridge Curve

Using the recent unemployment rate from the CPS and yesterday's JOLTS release, Corrections offers an updated Beveridge curve.

Don't judge the jobless

USA Today article "Don't judge the jobless" (October 27th, 2010) discusses "99ers", individuals who have collected extended unemployment insurance for 99 weeks and are about to run out. The author, while attacking Robert Barro who "doesn't know what it's like to be unemployed for this long," claims:

My story isn't unusual for young professionals.

It actually appears to be quite unusual. In order to see why, we can take general U.S. statistics as a first pass. Two questions are important to finding out if someone will be a "99er." The most important is "what are the chances an individual finds a job in a given month?" (Alternatively, "how long does it take to find a job?") We can examine the job finding rate per month as approximately equal to the number of unemployed re-entering the workforce. This isn't an exact statistic, as individuals may move from job to job, but it will be rather close. The number of jobs found in a given month over the number of unemployed for that month is displayed graphically below, and is known as the "job finding rate" (click to enlarge).


How might we interpret the above graph? As of August 2010, the number of hirings/unemployed was 0.32. That is, 1/3 as many people were hired as were unemployed. Extending this logic and making a few assumptions (homogeneity, only the unemployed are hired, both assumptions we shall defend as simplifying, but not result-altering later) that only the unemployed are hired, then the average individual should spend 3 months unemployed, or 13 weeks unemployed. 33% will spend one month, 22% will spend 2 months, 15% will spend 3 months, 9% will spend 4 months, and so on. To spend 22.77 months unemployed (99 weeks) comes with a very small probability-- 0.02%. Two hundreths of one percent is rather uncommon indeed. But this is slightly wrong for a number of reasons, though it is relatively accurate as a first pass. Say 30% of those new hires come from people moving jobs. We still have the probability 0.4%, or about half a percent.

First, the author notes that they were re-hired for a four-month stint before becoming unemployed again. We can ask a similar question: "What are the chances (making similar assumptions) that someone who was hired will last for four months?" We can find this from the "job loss rate", calculated as the number of fires, or separations (depending on your preference) displayed graphically below (click to enlarge).

In any given month, about 1.75% of currently-working Americans are fired, and about 3% separate from their job (for the interested, this gives about a 33-month average for a given job, reasonable when teenagers and young adults are added to the picture). In Correction's recollection, adults spend something approximating double that on a given job. What are the chances the author will be fired within four months of finding a job? Making similar assumptions, there's a 93.2% chance that an individual will not be fired before four months. That is, the chance the author would be fired within four months (or less) was 6.8%. While not as small a probability as a hundredth of a percent, this still puts her in a very small minority.

Corrections recognizes that these calculations assume a homogeneity that is not present. However, in the author's case, we actually think these assumptions have helped her. The inability to find jobs has fallen primarily on men, the uneducated, and construction workers. The author, formerly in the information industry, a woman with a college degree, will be less, not more common. Rather than attacking Robert Barro, who "doesn't know what it's like to be unemployed for this long" for a reason, and who wrote the (text)book(s) [1] [2] [3] on modern macroeconomics, the author would be better served by spending time looking for work. Her plight does not seem as common as suggested, and it appears rather difficult to rack up 99 weeks of unemployment, especially if one is college-educated and not in construction.

There is further data about unemployment insurance that Corrections has mentioned before ("Loss of Jobless Benefits Could Lower Unemployment Rate" July 6th, 2010). Even in the depths of Pittsburgh's recession in the early 80's, where local unemployment was higher than it is now nationally, individuals suddenly found jobs when their unemployment insurance ran out (click to enlarge):

On Course for a Cleaner Hudson

New York Times article "On Course for a Cleaner Hudson" (September 1st, 2010) discusses the best way to clean up polychlorinated biphenyls (PCBs) in the Hudson river. In a previous article, "Don't scorn Germany and Japan; learn from them", Corrections has extolled the near-incomprehensible properties of exponential growth. However, when the discount rate is greater than the growth rate, this may not be the case.

The E.P.A. now says the dredging might end up taking 10 years, which is fine. A job done slowly and right is better than one altered or abandoned.

Fortunately, we will not have to wait until the job is completed to see good things happen. When PCB concentrations start falling in the river, they decline in fish. This means the benefits of the project will start being felt long before the last load of toxic mud is pulled up from the bottom. This is the strongest rebuttal to G.E.’s old argument that the answer is to let the carcinogens lie in the river, decaying on their own.

If the cleanup of a river that has been tainted for 60 years and counting takes a few years longer than first planned, nobody should be complaining.

We can model the type of situation that the New York Times is suggesting. Specifically, we might have something we desire, say the Hudson River's stock of fish. We have two options for the same cost: quick cleaning and thorough cleaning. The growth rate of the stock of fish is increased to a higher long-term level due to thorough cleaning, but more slowly. It is increased to a lower long-term level due to quick cleaning. The difference between the changing growth rates is depicted graphically below (click to enlarge).

What would this mean for fish stocks? Normalizing our starting stock to one, we can display this graphically as well (click to enlarge)

However, we value current benefits more than we value future benefits--we discount exponentially. If our discount rate is greater than our growth rate, then it's quite possible that the net present value of "quick" is more valuable than "thorough". While exponential growth is a powerful force, exponential discounting may make slower growth now preferable to rapid growth later.

One way to illustrate this is to depict how much we value the first period, the first two periods, the first three periods, out to as many as we please. We do so graphically below (click to enlarge). As one can see, while the gap is closed, the net present value from today including any period in the future will always indicate quick growth as better.

Corrections simply notes, therefore, that a job done quickly is not always worse than a job done thoroughly--there are distinct tradeoffs even when considering exponential growth.

What if the end isn't near?

USA Today article "What if the end isn't near?" (August 23rd, 2010) discusses a large subpopulation in America that ostensibly believes that the Second Coming of Christ will occur within the next forty years. The article is deeply concerned about this and its effects on public policy (e.g. if Nuclear Disarmament or Global Warming are long-term threats, we need spend resources on them, as the world ends before they become problems).

A new poll from the Pew Research Center for the People and the Press finds that roughly four in 10 Americans believe the Second Coming will happen by 2050.

and

Thankfully, Wigg-Stevenson and many new-breed evangelicals like him are refusing the kind of end-times bait that lets believers off the hook — off the hook of inspired social action that can make their faith a powerful blessing to their society and their time.

Corrections, from its own a priori beliefs, finds this statistic difficult to believe. The proper economic method for discerning beliefs is to watch what individuals do, not what they say. Our a priori beliefs are so strong that Corrections suggests that individual economic activity simply doesn't match up with these beliefs--people are professing things to pollsters that they don't believe.Corrections ventures out of its area of expertise into christian eschatology to understand this poll figure. Any corrections are welcome; the purpose here is just to get a grasp on what individuals might believe, as various interpretations impact economic behavior.There are five important events or periods that are relevant to the Christian End Times: 1) The First Coming, 2) Tribulation 3) The Second Coming 4) The Millenial Reign 5) The Last Judgement.

1. The First Coming kicks off the sequence of events, bounding the sequence of events and marking the beginning of the "countdown".
2. The Tribulation is a period of time after the Rapture (taking of Christians to Heaven, and their disappearance on Earth). In this period of time, for many, the Four Horsemen of the Apocalypse come, many individuals die.
3. The Second Coming is the arrival of Christ on earth.
4. The Millennial Reign is the Thousand-Year Reign of Christ before Judgement Day.
5. Judgement Day is the point at which all economic activity ceases (e.g. August 29, 1997 as Judgement Day would signal the cessation of all economic activity, as individuals are separated into good and bad, and sent to the afterlife).

First, we stipulate all individuals believing in the Second Coming are Christians. In our understanding, there are several ways to interpret "The Millennium," mentioned in the bible before the Last Judgement (after which we suppose all economic activity to cease). These beliefs can be broken down into two categories and two sub-categories within those.The first is Premillennialism, which includes both Post-tribulational Premillennialism and Pre-tribulational Premillenialism. These believers hold that there is economic activity after the Second Coming--that the Second Coming occurs before the Millennial Reign.

In this case, these individuals do not believe that economic activity will cease upon the second coming. (Though Pre-tribulational Premillennialists may believe that the rapture will remove them or others from economic activity upon the Second Coming. Neither of these allows for the end of the world before 2040, requiring at least a Millennial Reign.

The second category are individuals who believe the Second Coming and the Last Judgement will be concurrent--in this case, all economic activity ceases. Included in this are Postmillennialists and Amillennialists, the former thinking that the Millennial Reign will occur before the Second Coming (and may have been happening for some time) and Amillennialists believing that the Bible only refers to a "symbolic" Millennial Regin. Both allow for the end of the world to occur in or before 2040.In any case, the article can only be concerning itself, as far as Corrections can see, with Postmillennialists and Amillennialists, as it would be difficult for either Premillenialists to believe the Second Coming will happen, due to the requirement of the Millennial Reign which has not happened--these people should still be willing to invest in their futures or their children's futures, as the Second Coming may happen in 2040, the world doesn't end.

Do people act as if the world will end by 2040 rather than at an indeterminate time? Corrections suggests not. To understand why, we merely need to understand that individuals would have starkly different consumption patterns. To understand why, take two individuals, starting out with the same consumable resource. They enjoy consuming it, but given they don't consume it, it grows or reproduces at some rate. An example of this might be any animal herding, or saving money (which grows at the real interest rate). Individuals are impatient, but also want to smooth consumption. One individual believes in an infinite-horizon world, where they save for themselves and future generations. Another believes the world will end in forty periods. How would their consumption patterns look? We solve the dynamic programming problem for when to sell a herd stock for both individuals. Their stock of animals and number of animals sold is displayed graphically below (click to enlarge):


As one can see, savings and consumption patters are starkly different in the two groups quite quickly--people who have dynastic preferences and solve an infinite-horizon problem (or something approximating it) are able to take advantage of exponential growth in a way that finite-horizoned individuals cannot. The question is whether or not we see this sort of behavior among the 40% of the population the Pew Research Center claims. It is also worth noting that the difference seen would be enlarged further by any comparison before today's date (we assume the same resources today--were individuals to have started with the same resources five years ago, a difference would be even more noticeable, because there is more time for divergence).

How might we see this in public policy? Any individual believing that Judgement Day would happen before 2050 and born after 1983 will not see any social security benefits, while paying in for social security and other retirement programs. Indeed, individuals born before 1983 will not come remotely close to being paid their contributions, and should rebel equally agianst this program.

Such individuals should not be saving for retirement, and certainly not be taking care of their bodies--many of this 40% who believe the world will end by 2050 should begin smoking, and planning for a family may be seen as mildly short-sighted.

In summary, Corrections believes that the lack of evidence on this 40% of the population, the lack of articles noting the incredible rise of unhealthy behavior and savings is evidence of individuals not believing what they claim to believe in surveys. Corrections might further note that while one may joke about short-sightedness among Americans today, the question is about whether or not people are behaving with the degree of extremity necessary to act as if the world was going to end in 40 years.

The Mackerel Wars: Europe's Fish Tiff With Iceland

Time Magazine article "The Mackerel Wars: Europe's Fish Tiff With Iceland" (Friday, August 27th, 2010) discusses optimal common-pool resource exploitation but speaks of "sustainable" fishing as though a balanced stock required a single and unchanging level of fishing.

The Marine Stewardship Council, which issues fishery certification programs, said that if the fishing continued at this rate, mackerel would start to fall below sustainable levels by 2012.

Let's imagine governments, along with the alphabet soup of NGOs the Time article mentioned (SFM, WWF, MSC, FIFVO, CFP, and PEG), are capable of optimally exploiting a common-pool resource. We can further imagine there are two possible stochastic states of the world: high price for mackerel and low price for mackerel. Additionally, there is a stock of fish that can be consumed, and after consumption, the remaining stock multiplies.

In this case, we might have a dynamic programming problem summarized by a value function with fish stock S, consumption C, price-state $$\theta$$, and price $$P(C,\theta)$$ and growth rate r:

With the law of motion for fish stock:

In this case, with appropriate parameters and functional forms, solving the value function above we may have a consumption pattern that has a non-singlet ergodic set for fish stock that is above zero. That is, in "low" price moments, we "under-fish." In "high" price moments, we "over-fish." Below, we graph out next period's stock against this period's stock under the high price and low price states (click to enlarge).

As one can see, the ergodic set stretches from where the 45 degree line (stock today is the same as stock tomorrow) intersects with a low shock (a stock cannot possibly go below this point, even with an infinite series of low shocks), to where the 45 degree line intersects with a high shock (a stock cannot possibly go above this point, even with an infinite series of high shocks).

The important stylized fact to understand from this is that it's possible not to have a "steady state" of fish but instead have an ergodic set of possible levels of fish, a similar notion that optimally exploits the resource, dipping into it in "bad" times and saving in "good."

Building Is Booming in a City of Empty Houses

New York Times article "Building Is Booming in a City of Empty Houses" (May 15th, 2010) suggests that the country has too many houses. While it gives some reasoning for this argument, the evidence for a bubble is not clear-cut to Corrections.

Simply put, the country already has too many houses, the legacy of wide-scale overbuilding during the boom. The Census Bureau says there are two million vacant homes for sale, about double the historical level. Fewer new households, moreover, are being formed as families double up for economic reasons, putting a further brake on demand.

Was there a housing bubble in prices? Was there a housing bubble in construction? One might ask, as Casey Mulligan has (our analysis is indebted to him), whether or not these oft-cited bubbles are really bubbles--the answer is not immediately apparent to Corrections. There does not appear to have been a particularly spectacular housing boom in terms of new housing units or housing completion, judging from the biannual American Housing Survey. The housing bubble is often cited to have started in 1996, when the Case-Shiller Housing Index first began to rise dramatically. However, it appears as though half of the dramatic rise in prices from 1996 has survived the "bubble's" burst--indicating that at least some portion of the bubble was not a bubble at all, but driven by some fundamentals. Housing Units from the American Housing Survey are displayed below, along with the composite Case-Shiller Index, Housing Completions from the Census, and Residential Investment from the Bureau of Economic Analysis's National Economic Accounts (click to enlarge). Housing Units for 2009 is due Summer 2010--the value displayed is imputed from housing completions over a period of 20 years, and some interstitial data points are similarly linearly imputed. An update will be offered when the American Housing Survey for 2009 is released Summer 2010.



As one can see, the stock of housing units never increased dramatically--15% at their peak. The flow of housing completions and residential investment both grew and have fallen from their peak. However, prices have not fallen completely, which indicates to Corrections that the "bubble" was not necessarily a bubble, but simply a housing boom, driven at least in some part by fundamentals--were it not, prices would be even lower than they are now, given an increased housing stock.

Consider the evidence

Philadelphia Inquirer opinion editorial "Consider the evidence" (December 21st, 2009) ignores an interesting possibility concerning the delay in police departmental testing of rape kits. The article is perturbed that there is a shortage in processed rape kits.

The backlog of untested kits includes about 12,500 in Los Angeles, 10,000 in Detroit, 6,000 in San Diego, and 4,000 in Houston. (Philadelphia police, to their credit, say their lab tests every kit).

And

Money shouldn't be a roadblock to solving these crimes. Congress passed a law in 2004 to provide grants to states for rape kit testing. But the law allows police departments to use the money for other DNA testing, not just rape kits. Human Rights Watch reported last March that the Los Angeles Police Department's backlog of untested rape kits occurred despite LAPD's receiving $8 million in grants for testing during the previous four years.

There is no explicit price mechanism to clear the market for processed kits, so instead it is cleared by the implicit price mechanism of time-to-process (perhaps mixed with a nebulous definition of priority). Furthermore, supply is constant. If we increase supply, we expect waiting time to decrease in the short run. However, in the long run, prosecutors and police change their standard methods of operation, and increase their use of more sophisticated methods. This, in turn, raises the waiting time. If long run elasticity is very high, we expect supply shifts to only ever shift waiting time a little. Such a case is depicted graphically below (click to enlarge).  Additionally, our expectations on the evolution of "price" and quantity over time are depicted below (click to enlarge).  

It is foolish to focus only on waiting time or backlog--instead, optimizing behavior would be to first minimize the sentence-adjusted cost of bringing in a suspect (which may include many rape kits or few rape kits), and then choose the amount of money one wants to spend, setting the sentence-adjusted marginal benefit to our (minimized) marginal cost.

Pittsburgh Sets Vote on Adding Tax on Tuition

New York Times article "Pittsburgh Sets Vote on Adding Tax on Tuition" (December 15th, 2009) provides an inadequate analysis of the consequences of Pittsburgh's proposed tax on tuition:

On Wednesday, the City Council is expected to give preliminary approval to Mayor Luke Ravenstahl’s proposal for a 1 percent tuition tax on students attending college in Pittsburgh, which he says will raise $16.2 million in annual revenue that is needed to pay pensions for retired city employees. Final Council action will be on Monday.

When considering the tax, there are three aspects to consider: the marginal student's decision, the marginal dollar of the University, and the incidence of the tax.

The price elasticity of demand for education from Carnegie Mellon (and other colleges in Pittsburgh) is likely quite elastic, while price elasticity of demand for education is likely to be highly inelastic. Goods become more elastic as fraction of expenditure increases for normal goods like education. Therefore, we expect full time students, poorer students, and students with less lifetime income to be the marginal exiting individuals. We might expect Carnegie Mellon's english students to leave the program more quickly than its engineering students. We expect that "national" students are more elastic than "local" students and would leave more quickly. In the long run (presumably four years as the pre-tax stock of students fully depreciates) the composition of local colleges will change, presumably to include more wealthy and local students.

The price elasticity of supply for education from Carnegie Mellon (and other colleges in Pittsburgh) is likely to be relatively inelastic in the short run and relatively elastic in the long run, especially as the composition of students shifts.

The incidence of the tax, therefore, is likely to fall primarily on Universities at first, and, as it is able to shift capital and become a more local university populated by wealthier students.

Correction's conjecture about the direction of our four relevant variables is graphically displayed below (click to enlarge).

Tough Times for Big Law

Wall Street Journal opinion editorial by Elizabeth Wurtzel, author of Prozac Nation "Tough Times for Big Law" (December 14th, 2009) concerns itself with a number of recruits for the law firm Cravath, Swaine & Moore.  Last year, every single one of those recruits turned down an offer of $80,000 plus student loan and benefits, not to work and be put on a furlough of sorts until the economy recovered.  Wurtzel is particularly concerned by this development:

...here's something weirder: I've been told that none of the graduates of Yale Law School who were headed for Cravath accepted their offer of $80,000 to surf and sunbathe, or go forth and save the world. Since no one at either institution is willing to discuss this—and I don't blame them, because I would be embarrassed too—I don't know this for certain. But here's what I'm sure of: Not everybody took Cravath up on this peachy keen opportunity to do anything for a year with pay and benefits. And that by itself is disturbing enough.

If even one person said no to $80,000 for bubkes, I'd question the sanity and intelligence of that sole holdout. Cravath recruits the best and the brightest kids from the most highly ranked law schools—and given $80,000 and a dream, all many of them could do was report to work on Monday.

Yet Wurtzel, in her acidulous censure of youth's follies, overlooks the possibility that human capital depreciates. If knowledge concerning Miss Wurtzel's jejune Uniform Commercial Code and the Rule Against Perpetuities is a function of use of that knowledge in the period previous to this, as well as a costly means to re-obtain it (presumably studying) then individuals may want to keep that capital from depreciating in the cheapest way possible. This may include paying to work, if their human capital is valuable enough and reconstructing it from non-use (i.e. from studying) is costly enough.

We may add, more trivially, that the lion's share of payment for entry-level individuals at Cravath, Swaine & Moore is in all likelihood not their benefits, nor their salary, but instead the future expected value of a path that brings them to be a partner in the firm, or signal their value to other firms and clients.

Oh, for the sounds of hammers

San Diego Union-Tribune article "Oh, for the sounds of hammers" (November 21st, 2009) appears to miss the special nature of durable goods like housing in the "business cycle." The government should not delay our arrival at a long run housing market equilibrium by building more.

One, be thankful for complex civic projects, the kind that take longer to complete. We’re talking about Vista’s new civic center, fire stations and amphitheater or Escondido’s new police station, almost finished. Or school bond issues, passed last November. The money’s available, but winning state design approval takes time. Districts that act nimbly will be able to stretch their dollars by purchasing material and talent while prices are low. Public projects will keep the construction industry alive while the private sector struggles to shake off the bust part of the boom and bust cycle. [Emphasis added]

Buildings last a long time. We build a very low percentage of houses that go into the market every year, because houses last so long. If we have, due to a shift in our expectations about the need for construction, built too many houses, too many office buildings, too many McDonalds, it must be recognized that it will take some time for us to shift supply back down. We have to wait for enough buildings to depreciate so that we are back to a lower, more appropriate steady-state. Until then, we find ourselves in a situation where investment is zero (or very low), as depicted below.

The government can do one of two things to stimulate the sound of hammers: it can commission public woks projects or it can build houses (for example, by subsidizing building costs for new houses). The government should not to to prop up the construction industry by encouraging public works projects because these projects are already at their steady state (there was no famous public works bubble). If government, on the other hand, props up the housing market by building houses out of equilibrium, they will delay investment. This is because by increasing the quantity of new houses on the market to above equilibrium levels, the government causes the price of housing to remain lower for a longer period of time. This means that the "steady state" time period depicted below (click the image to enlarge) occurs later than it would without government intervention. Ultimately, we see no reason for the government to force such suboptimal levels of production.