The Search-Matching Theory of Unemployment

This Commentary from the Cleveland Fed explains the search-matching theory of unemployment and shows how it can be used to predict how changes in unemployment compensation, taxes, or technology might affect the unemployment rate:

Understanding Unemployment, by Guillaume Rocheteau, Federal Reserve Bank of Cleveland: A disturbing feature of the labor market is its seeming inability to clear. At each instant in time, there are both workers without jobs and jobs without workers. How can it be that productive resources are left unemployed in a well functioning market economy?

Economists attribute the failure of the labor market to instantly allocate workers to jobs to various “frictions.” These frictions arise because labor, unlike gold or oil, is not a homogenous commodity. The services provided by a plumber are different from those provided by a lawyer—and even lawyers differ in the services they offer; some specialize in constitutional law, others in private law. To match jobs and workers is far from a trivial problem. The heterogeneity of labor services also makes it hard for employers to distinguish productive from unproductive workers. And to complicate things even more, the mere process of moving labor services from one job to another is not costless.

Over the past 25 years, economists have developed a theory of the labor market that takes into account the heterogeneity of labor services and that describes the matching process of workers and firms. The theory, sometimes called the search-matching theory of unemployment, is the description that most economists have in the back of their mind when thinking about the labor market. In this Commentary, we review this theory and show how it can be applied to address several issues related to unemployment.

■ Three Building Blocks for a Theory of Unemployment

The search model of unemployment contains three elements. Each element characterizes a different aspect of the labor market, and the three elements together determine the behavior of the overall labor market. The first element describes how wages are set. The second determines the number of vacancies that firms decide to open, and the third describes the process through which unemployed workers and vacancies are brought together, that is, the process of creating jobs.

Setting Wages

Not all labor markets work the same, but in many, wages are determined through a bargaining process between workers and their employers. The outcome of the bargaining process depends on two things: the bargaining power of each party and the outside options of each. The party with the most bargaining power—the worker or the firm—is the one that can extract a larger fraction of the surplus that stems from their relationship. The outside options for both workers and firms depend on the income of each if they stay unmatched as well as their ability to locate alternative partners if the negotiation fails.

Outside options are affected by the “imbalances” of the labor market—the number of vacancies and the number of unemployed workers. Wages respond to changes in outside options as follows. If the number of vacancies per unemployed worker (a measure of the scarcity of workers often referred to as labor market tightness) is large, then workers’ outside options are good and they can ask for a high wage. Firms are willing to pay this high wage to avoid having to look for another worker and incurring high recruiting costs. But if vacancies are scarce relative to unemployed workers, then workers’ outside options are poor, and they are willing to accept low wages to avoid a long spell of unemployment.

In cases where wages are formed differently than by bargaining between workers and firms, most descriptions of the wage-setting process would still predict that wages tend to increase as the number of vacancies (per unemployed worker) increases. The relationship between the wage and the number of vacancies is referred to as the wage-setting curve and is shown in figure 1. Our version of the wage-setting curve slopes upward: As the number of vacancies increases, workers get higher wages.

Click on figure for pop-up version

The wage-setting curve shifts to the left or the right when fundamentals of the economy change. For instance, the curve moves to the right—meaning that wages increase—as workers’ productivity increases, as workers enjoy more bargaining power, or as they receive more generous unemployment benefits.

Opening Job Vacancies

Once we know how the market wage is determined, we can find the number of workers that firms are willing to hire, or equivalently, the number of vacancies they want to open. If it were costless to find a suitable worker and if it could be done instantaneously, firms would keep hiring workers as long as each new worker’s productivity exceeded the market wage. But hiring a worker is neither costless nor instantaneous. The firm needs to post and advertise a vacancy, evaluate candidates, and so on. As a consequence of these labor market frictions, a firm will want to open a position only if the sum of profits it makes by hiring a worker compensates it for the various recruiting expenses it incurs to find the worker. This condition is referred to as the vacancy-supply condition. It says that the number of vacancies opened in a labor market is determined as a function of the market wage and recruiting costs.

The vacancy-supply condition is represented in figure 1. The curve slopes downward, meaning that the number of vacancies falls as the wage increases. This can be understood intuitively by considering that when the wage is low, each worker generates high profits, and firms are willing to open a large number of vacancies. Of course, as the number of vacancies increases, it becomes harder for firms to find workers. As a consequence, hiring and recruiting costs increase until the incentives to open new vacancies are exhausted.

Again, changes in the fundamentals of the labor market can affect the position of the vacancy-supply curve. The vacancy-supply curve moves upward (which means that firms want to hire more workers and therefore open a larger number of vacancies) as workers become more productive, as the cost of advertising vacancies falls, and as the process of finding suitable workers becomes more efficient.

Matching Workers and Jobs

The wage-setting curve and the vacancy-supply curve allow us to determine the wage and the number of vacancies opened by firms. This information, however, is insufficient to determine the unemployment rate. We need to know how the number of vacancies affects unemployment. For this, we need to understand how vacancies and unemployed workers are matched to create filled jobs.

As outlined earlier, the mechanism through which workers and firms are matched is imperfect and time consuming. Formally, this matching process is described as a “productive” process. There is an output: the number of matches between workers and firms, or equivalently, the number of jobs created. There are two inputs: the number of unemployed workers and the number of vacancies. The relationship between the stock of unemployed workers and the stock of vacancies to the number of jobs created, the so-called matching function, has been estimated for the U.S. economy (as well as for other economies). It has the following properties. The number of jobs created is larger when there are more unemployed workers and vacancies. This property can be understood intuitively when you consider that a productive process produces more output if it has more inputs. If one doubles the number of vacancies and the number of unemployed workers, the number of jobs created should be doubled as well. (The matching function is said to have constant returns to scale.) However, the rate at which an unemployed worker finds a job decreases as the pool of unemployed workers expands. Economists say that workers exert a “congestion effect” on each other when they are searching for a job. The matching function is illustrated in figure 2. The flow of job creations feeds the stock of employed workers and filled jobs. The stock of unemployed workers is replenished by the flow of job destructions.

Click on figure for pop-up version

If the economy were not subject to various shocks, it would end up in a steady state, where the number of jobs created would equal the number of jobs destroyed, and the stock of unemployed workers would remain unchanged. In this steady state, the unemployment rate would be low if the flow of job creations were large relative to job destructions, which would occur when the number of vacancies was large. But if there were few vacancies, then the flow of job creations would be small, and the unemployment rate would be high. The negative relationship between vacancies and unemployment (at the steady state) is represented in the right panel of figure 1, and it is called the Beveridge curve.

The Beveridge curve is an important tool for economists who want to assess the extent of search-matching frictions in the labor market. An upward shift of the Beveridge curve is symptomatic of a more severe mismatch problem between workers and jobs.

Putting the Three Building Blocks Together

Obviously, wages, vacancies, and the unemployment rate cannot be explained independently. One cannot understand wages without knowing the tightness of the labor market; the number of vacancies depends on the market wage; and the unemployment rate depends on the number of vacancies opened by firms. We have to put the three pieces of the puzzle together.

Since the vacancy-supply curve slopes up, and the wage-setting curve slopes down, there is a unique intersection between the two curves. The point of intersection determines the going market wage and the number of vacancies (that is, the vacancy-unemployment ratio. See the left panel of figure 1). The market wage is denoted W* in figure 1, and the vacancy-unemployment ratio is denoted V*. Once we know the vacancy-unemployment ratio, the unemployment rate is obtained from the Beveridge curve (see the right panel of figure 1.) The equilibrium unemployment rate is denoted U* in figure 1.

We can then use this simple theory to determine how the equilibrium unemployment rate is affected when economic fundamentals, such as productivity, workers’ bargaining power, recruiting costs, and matching frictions, change or when policies, such as unemployment benefits or taxes, are altered.

■ The Determinants of the Unemployment Rate

Generous unemployment benefits are often blamed for higher unemployment rates in Europe relative to the United States. How valid is this claim? The search-matching theory can help us evaluate it. According to the theory, higher unemployment benefits shift the wage-setting curve to the right: Workers are in a better position when unemployed, which allows them to negotiate a higher wage. As a consequence, firms have a lower incentive to open vacancies because they would make lower profits off of them.

More generous benefits can also slow down the time it takes to match workers and firms. First, unemployed workers are in less of a hurry to find a job and, therefore, they search with a lower intensity. Second, they are more choosy in terms of the type of job they will accept. Because of these effects, the Beveridge curve shifts upward, and for a given vacancyunemployment ratio, the unemployment rate increases. To summarize, more generous benefits lead to higher wages, fewer vacancies, and slower matching. No surprise, the unemployment rate increases.

More powerful European unions have also been blamed for transatlantic differences in unemployment rates. Do unions deserve such blame? The search-matching theory says that the higher bargaining power enjoyed by unions in some European countries allows workers to extract a larger share of the surplus generated by a job. Because the market wage is higher, firms have a smaller incentive to open vacancies. Graphically, the wage-setting curve shifts to the right, which raises wages but reduces the supply of vacancies. Unemployment increases.

Some economists have argued that the main reason unemployment rates differ across developed countries stems from different tax policies. For instance, payroll taxes tend to be higher in Europe. According to the search-matching theory, taxes reduce firms’ incentives to open vacancies and workers’ incentives to search for jobs because taxes reduce the (net) surplus from a filled job. Graphically, a payroll tax moves the vacancysupply curve downward and the wage-setting curve to the left. The vacancy-unemployment ratio and (net) wages are lower, while unemployment is higher.

Countries with similar policies can have different unemployment rates because they use different technologies to match workers and firms. The Internet or employment agencies, for example, might improve the matching process, and firms in countries where they are available will have higher incentives to open vacancies. Graphically, the vacancy-supply curve moves upward. The vacancy-unemployment ratio and wages increase. In addition, the Beveridge curve shifts downward because the matching process is more efficient. Therefore, the equilibrium unemployment rate is lower in countries with lower matching frictions.

■ Why Do Unemployment Rates Vary with Business Cycles?

Unemployment rates are lower in booms and higher in recessions. The search theory of unemployment helps makes it clear why this should be the case. Business cycle fluctuations are commonly thought to be initiated by productivity shocks, and changes in labor productivity over the business cycle will cause predictable consequences in the labor market that are captured by the theory. What happens when workers become more productive? Because they produce more output, they can ask for a higher wage. The wagesetting curve moves to the right. Firms also make higher profits when workers are more productive (assuming that workers cannot appropriate the full increase in productivity), so the vacancy-supply curve moves upward.

Click on figure for pop-up version

Over the business cycle, the vacancy rate will cycle above and below the Beveridge curve (see figure 3). A positive productivity shock raises the vacancy-unemployment ratio so that the economy is located above the Beveridge curve. Then, the unemployment rate decreases over time and the economy returns to the Beveridge curve. Similarly, following a negative shock, the vacancy-unemployment ratio falls and the economy falls below the Beveridge curve. Then, the unemployment rate increases gradually to bring the economy back to a steady state.

The Beveridge curve can also shift up and down during the business cycle. Indeed, recessions are often described as intense periods of reallocations of workers and jobs. One explanation for this phenomenon is that the reallocation of jobs is less costly during recession because the opportunity cost of closing jobs and plants (the foregone output, worker retraining, the retooling of plants…) is smaller than it is during booms.

■ Recommended Readings

Dale Mortensen, and Christopher Pissarides. 1999. “New Developments in Models of Search in the Labor Market,” Chapter 39 in Orley Ashenfelter and David Card (eds.) Handbook of Labor Economics, vol. 3B, Amsterdam: North-Holland.

Christopher Pissarides. 2000. Equilibrium Unemployment, 2nd edition, Cambridge, Mass.: MIT Press.

Material may be reprinted if the source is credited.

Comments

[reason]

Well yes sort of. But isn't this a very incomplete analysis. You also have to explain arrivals on the job market and the effect of employed persons looking for a better job and there is no explaination at all about what determines the general level of vacancies apart from vague talk about profitability of a job possibility. And no statistical tests.

It offers an explaination as to why vacancies may be filled faster with lower unemployment benefits but noting that they will be filled at a lower wage level and with a worse match (probably for both sides) it is not clear that it is the better option from a social welfare point of view. It is the old story, choose the wrong target and you may be sorry if you get what you were after.

[joan]

This is a theory about wages as well as unemployment. According to this theory the government/fed can keep wages low. First by providing an excess of workers (immigration, guest workers). Second by running large deficits during booms putting pressure on the fed to raise rates damping the boom and preventing unemployment rates from falling below the "natural rate". Then capital captures the the gains from the increase in productivity. If you can create the deficit by cutting taxes on the rich even better. Look at graph at
http://www.visualizingeconomics.com/
keeping in mind that the US debt/gdp fell from WWII to the 1970's and has doubled since then.

Some qoutes from paper:
"Business cycle fluctuations are commonly thought to be initiated by productivity shocks, and changes in labor productivity over the business cycle will cause predictable consequences ..... What happens when workers become more productive? Because they produce more output, they can ask for a higher wage.......But if vacancies are scarce relative to unemployed workers, then workers’ outside options are poor, and they are willing to accept low wages to avoid a long spell of unemployment."

[reason]

One explanation for this phenomenon is that the reallocation of jobs is less costly during recession because the opportunity cost of closing jobs and plants (the foregone output, worker retraining, the retooling of plants…) is smaller than it is during booms.

Has this guy ever been in the real world. The real reason is that it is easier to get away with it. If you cut back during a boom, your reputation is mud and if you want somebody you have a tough time finding somebody. If you cut back when everybody else does, well "times are tough, lad". It is the same as the famous Keynes quote about the secret to being a prudent banker is to be inprudent in the same way as everybody else. Why don't firms just reduce hours/wages or encourage unpaid leave during recessions? Just asking!-)

[calmo]

Some statements like this one:A disturbing feature of the labor market is its seeming inability to clear. are particularly self-descriptive. That is, this statement itself has a seeming inability to clear. As if all murky puddles eventually settle to some transparent state...as if a few more sentences will provide that clarity. (Are you still reading?)[This could be a total waste of your precious time...a lashing from the sadistic Thoma then?...haven't had a lashing from him in ages!] So we tyros are invited to continue in our quest to find out what this could mean and it is:At each instant in time, there are both workers without jobs and jobs without workers. How can it be that productive resources are left unemployed in a well functioning market economy? So good to have it confirmed that we are not ants on a hill, but troubling (Are you not troubled, little ant?) that the expressions, "at each instant in time" and "left unemployed" led us astray from that mission to clarify those Heraclitean (not the hair spray) moments of flux from those well-trained but nonetheless, rotting carcasses on the road side of an otherwise fresh-smelling "well-functioning market economy".
So there was some clarifying afterall in the introduction, yes? We have a sense of what the problem is and the dynamic difficulties, yes? The non-ant-like market economy functioning more or less sub maximally owing to the ant-like abilities of trained workers who have not had their professional development course in the last week and therefore are at risk of becoming a carcass, yes?
Apparently there is a substantial literature Over the past 25 years, economists have developed a theory of the labor market that takes into account the heterogeneity of labor services and that describes the matching process of workers and firms. and it appears the wayward ants have not gone unnoticed, nor the study, untitled.The theory is called the search-matching theory of unemployment, It does make this wayward ant feel like he might be missing the ant-hill somehow, you (fellow ant)? Will the next paragraph or 2 set me back on course? I escape now only to avoid truncation --I may not be a well-trained ant, but I am experienced.

[cm]

The model assumes only two inputs to firms' matching process -- the unemployed (i.e. more generally available workers), and open positions, which implies the "matching effort" is efficient/effective (i.e. a possible match will convert to an actual match) and can scale indefinitely.

This is not the case, and as I have argued in the past, at employers who are buy appearances (eventually) willing to pay up (something that undoubtedly some will dispute is wiedspread), a significant ingredient in "not finding" qualified workers is not devoting enough or effective efforts to performing the match.

The presence, or perception thereof, of a large number of workers (unemployed as well as job-changers) competing for relatively few openings leads to the (understandable) attitude of "we want top talent", and consequently aiming too high, while assuming all the top talent (which by definition is in short supply) will come exactly to you (presumably because yours is the greatest company in the field, and offers the most gratifying jobs and best career growth), and it is easy to tell the wheat from the chaff, in fact so easy that it can be done by computer software keyword-matching resumes. And because of that, you don't need to arrange for your hiring managers to actually have or spend the time to sift through resumes, phone screens, and interviews to "evaluate" all or at least many of the applicants. And once you hit on talent, you can lowball, because where else are they going to go, right?

[evagrius]

Is this guy some French refugee or something? Suspicious name, if you ask me :)

[Richard]

I'd be interested in a meaningful discussion of _changes_ in the labor market.

As positions have become more finely differentiated over time, filling those positions should be more difficult. To oversimplfy, if there were only two types of labor 150 years ago (call them farmer and worker), and today there are 20,000 positions just as differentiated, you would expect that the matching would become much more difficult.

[georgist]

Has this guy ever been in the real world. The real reason is that it is easier to get away with it. If you cut back during a boom, your reputation is mud.

This argument is suspicious. It seems to me that cutting during a boom would be better for one's reputation, since the workers who got laid off would have an easier time finding another job. The same goes for bankers all taking the same kind of risks - why would reputation mechanisms lead to such perverse effects?

[slink/js paine]

i like the ant farm notion calmo

mermidons without an achilles

[calmo]

farm? what farm
wazzat o slink?
I be bulletted
down by the
3 Elements
letting The
Model have
its way
with me
and hardly
noticed.
It B
such a cruel
world out....there.

[cm]

Richard: Yes, specialization and sophistication of occupations has increased. So has specialization and sophistication of the job-matching process and its tools, and the labor supply for most positions has expanded, both in terms of available skills (more penetration of education and vocational training than centuries ago), and geographically (firms can pretty much source/advertise nationwide, and across borders).

All nominally of course. If firms "choose" not to make full use of the potential of better job-matching, or don't offer good enough relocation, signing bonuses, or basic compensation to begin with, they will find it difficult to fill their respective 100's different types of positions. More so when they strongly prefer to hire job-switchers over the unemployed or fresh out of school.

[cm]

Re job-switchers, we have been through this many times. In "mature" industries with "commodity" jobs, why should somebody switch from job A to roughly the same job B, in roughly the same type of company with roughly the same compensation and roughly the same career outlook, if not for personal reasons?

If I'm let's say a senior engineer here, what is the point in switching to a senior engineer position there where I can expect to be doing pretty much the same as what I'm doing now, and they pay precisely "industry standard" wages and benefits? They may think I'm a commodity, but so are they from my perspective.

I have heard from some attempting to switch sub-industries that some prospective employers are asking for a substantial pay cut, on the grounds of not being supremely experienced in the specific tools/technologies used in those jobs. Some will take that, but typically only when they really want (or have) to get out from their old place. That tells me that the employers consider them qualified enough to be hired. In the specific cases I refuse to believe there are no better qualified takers, firms just don't want to pay up.

[reason]

Georgist...
It seems to me that cutting during a boom would be better for one's reputation, since the workers who got laid off would have an easier time finding another job. The same goes for bankers all taking the same kind of risks - why would reputation mechanisms lead to such perverse effects?

Can't have positive feedback effects in our equilibrium model can we? Why do you rule something out because it implies a perverse effect? Perverse effects are common in reality. Do recessions never happen, or booms?

I think you are forgetting about the risk and cost of changing jobs.

Think about from the point of view of somebody taking a risky and costly (but eventually rewarding?) step of changing firms. More likely in a boom (when firms are actively recruiting and throwing money around). A history of insecure employment ("even in good times!") is definitely not a plus in evaluating a prospective employer. Given that recessions occur less frequently than good times, cut backs during recessions are more easily forgiven. I know this is the case, otherwise why is there always a boom in big redundancy announcements during recessions, often closely correlated in time? Why wouldn't firms just steadily reduce there workforces instead of in big bursts? Answer: they want to have a good excuse, precisely for reputation reasons.

[reason]

Georgist...
Besides, firms don't need lay-offs during booms - they can get rid of workers just by not giving them raises or bonuses.

[ninjaplease]

"Georgist...
Besides, firms don't need lay-offs during booms - they can get rid of workers just by not giving them raises or bonuses."

This is a lot easier than firing someone which may induce legal action, and its a lot cheaper than severance.

[Barry]

Or just pile the work of a departed worker on them (or even better, the work of several departed workers). That'll make them leave.

If you're worried about inefficiency/errors, just pile on the unneccessry gruntwork of the departed workers on the target. The neccessary work gets split among several remaining workers, so that they are less likely to leave, and the work is less likely to be botched.

[cm]

reason: Layoffs are always unpleasant, at least at the lower levels of the organization where everybody knows everybody else. During "good times", when by definition corporate earnings are (relatively) good and books are full, fewer questions about "redundancies" will be asked, and few want to be the first to voluntarily reduce the size of their "empire".

[reason]

cm...
What you say is true, but big layoffs are decided in the boardroom, by people who have been deliberately selected for ruthlessness. I think reputational effects are the big issue for them.

[cm]

reason: That is not untrue, but division chiefs, directors, etc. have a word to say too, if they so choose. At no level in the organization will anybody in their right mind needlessly create trouble or piss off their subordinates (at least those they depend on, and whom they would like to stay for a while). Places where that happens, for idiocy or macho "culture", tend to be dysfunctional, and it invariably shows, unless their position in the market is invincible (for the time being).