The value of search-and-matching models for the labor market

University of Queensland economics professor John Quiggin of Crooked Timber recently published an excellent blog post questioning the usefulness and empirical success of the dominant macroeconomic model of the labor market: the search-and-matching framework.  Peter Diamond of the Massachusetts Institute of Technology, Dale Mortensen of Northwestern University, and Christopher Pissarides of the London School of Economics won the Nobel Prize in Economics in 2010 for their foundational work on this model. Most recent theoretical and empirical work on macro labor markets, including my own dissertation, is based on it because it was the best thing economists had on hand when the world came calling to ask about unemployment in the Great Recession.

Moreover, several high-quality datasets that track the model’s observables have also become available in recent years and have enabled important empirical work based on investigations of the model’s predictions and the implications of their success and failure. But Quiggin’s critiques are well taken, and have sparked an interesting conversation, with contributions from Stony Brook University economist Noah Smith, the Roosevelt Institute’s Mike Konczal, and others. Why is it worth having this discussion? Is this just an ivory tower academic debate about oversimplified mathematical formalizations with no empirical basis?

On the contrary, a correct understanding of the labor market is of central importance to assessing its ailments and ordering the right prescription. And the labor market is the way that the majority of people earn the majority of their living, although that living has gotten more meager for all but the top few over the past several decades. The middle fifth of the household income distribution earned labor income of $45,315 in 2011 dollars, or 77.1 percent of their total income, in 1979, and only $45,997 (amounting to 65.8 percent of their income) in 2007—a mere 1.5 percent increase despite a 129 percent increase in inflation-adjusted gross domestic product. The overall share of national income going to labor has declined from 79 percent in 1979 to 71 percent in 2010.

The search-and-matching model works like this: one class of agents, “workers,” is either searching for a job or employed while another class of agents, “firms,” is either vacant, meaning it has a vacancy posted, or filled, in which case it employs a worker and together they hum along productively. In the earliest formulation of the model, the only economic decision made by either agent was whether a firm would post a vacancy in an attempt to match with a worker or would choose not to, thus remaining inactive. Otherwise, both searching workers and vacant firms mindlessly wait until they match up, then commence a productive relationship that lasts until their match spontaneously dissolves. Then the worker goes back to searching and the firm makes its decision about whether to post a vacancy or not once again.

The reason why search-and-matching labor market models have something to say about the recent history of the labor market is because they are a good deal richer than the simple search-based story, which is the reason why Federal Reserve Bank of Richmond economist Karthik Athreya, whose book sparked this discussion, said that “search is not really about searching.” Specifically, they allow for alternative theories of wage-setting, a factual timeline for unemployment spells and what determines their duration, a rich set of labor market outcomes beyond employment and unemployment, and an implementable notion of power that is often a critical missing piece of economic modeling.

Like all economic models, the search-and-matching model is a simplification, even a ludicrous one. Quiggin argues that it fails even as a simplification of reality because the main reason why unemployment exists is not because workers and firms are groping in the dark for one another, a process which just by its nature takes time. And he’s right about that. So do we search theorists have a big problem?

Notice that my summary of the model left out one big thing: how the fruits of the productive employment relationship are split between the worker and the firm. This is by far the biggest controversy in the field of search theory. The assumption made by the earliest search-and-matching models is that the “surplus” the two agents generate is split between the parties in the optimal way, where the optimality concept is defined within the model but with some relationship to a more general intuition about what each party would want. (That optimal way is known as the “Nash Bargain” after the Nobel-Prize-winning mathematical theorist John Nash, the protagonist of the film A Beautiful Mind.)

The problem is that this theory of wage setting is an empirical disaster. Not only is it inconsistent with investigations into how actual wages are actually set, but it generates false predictions about unemployment spells that crucially fail to line up with what happens to unemployment during recessions (it goes up, and it stays high for a long time, when the optimal theory of wages says that wages should do the adjusting). Refinements that make the theory with Nash Bargaining consistent with the data on unemployment in recessions yield their own big empirical problem: those refinements imply that being unemployed isn’t really that bad for workers, which everyone who is sentient knows to be untrue.

So the search-and-matching model has a crazy theory about how wages are set, and that makes it a crazy model of how labor markets work, right? No. What the search-and-matching theory has, and what its alternatives lack for the most part, is indeterminacy about how wages are set. The “Nash Bargain” theory is optimal, but it’s not necessary—other wage-setting assumptions can be used to resolve the indeterminacy. And if economists can get their minds around the idea that the “market solution” is not always optimal then they can make real headway with the search-and-matching approach precisely because it’s consistent with those alternatives.

That’s where the most promising research into the macro labor market is happening. If wage-setting in the search-and-matching model is made more factual by including what seems to be the well-established norm of not actually cutting pay in nominal terms, then it generates long unemployment spells and high unemployment rates—not because something about the matching process has become more inefficient, which Quiggin is correct to call absurd, or because workers don’t care whether they’re employed or unemployed— but because the labor market is a great deal stickier than the canonical competitive equilibrium model assumes.

The search-and-matching model boasts several other strengths. In the popular imagination (mostly of those who have never been unemployed), unemployment follows a large-scale layoff. Basically, it’s the destruction of employment that leads to high unemployment. But in reality, high unemployment occurs mostly when the hiring rate declines. The overall job separation rate is, in general, not related to the business cycle, and it has been in long-run decline, which is itself evidence of ill health in the labor market. There was a very transient uptick in mass layoffs during the 2008 recession, but the market reverted to its long-run level of around 1.2 percent laid-off per month as the official recession ended in late 2009.

Hiring, on the other hand, went down at the beginning of the recession and has remained lousy for a long time. The factual way to interpret this is that there’s inherently churn, or movement in the labor market as workers quit jobs or get laid off and are hired for a new job. The labor market is unhealthy when the workers who leave their jobs can’t find new ones. That is a story that can’t be told without a search-and-matching model.

Furthermore, modifications to the search-and-matching model allow it to explain numerous other phenomena. Instead of workers being only either employed or unemployed, non-employed workers can be allowed to exit the labor force entirely, to go on disability, or to remain in traditional unemployment (that is, receiving unemployment insurance while searching for a job), or enter some other unattached state. Employed workers can be allowed to remain happily with their existing firm or look for a new job while staying employed at the old one. These elaborations obviously allow for a richer set of predictions, and they also let trends such as a prolonged slack labor market to manifest themselves in more ways than high unemployment and/or low wages, including the reduced size of the labor force and more job-lock as those lucky enough to have a job cling to it tenaciously.

Another strength of the search-and-matching approach, and one that is essentially an implication of the indeterminacy of wages, is that it has room for the concept of power, which alternative approaches, especially the competitive equilibrium, do not. In the Nash Bargain, there’s an explicit mathematical parameter that captures the relative power that workers and firms have in the wage-negotiation process. That alone is not terribly meaningful because if anything is an endogenous concept requiring an explanation rather than simply a mathematical assumption, it’s power.

But power also works its way into the model through what are known as the parties’ threat points, meaning the alternatives each agent has available when they are negotiating. When the labor market is weak and unemployment is high, the threat point for workers deteriorates, which means they can be squeezed by firms, a phenomenon that captures a great deal of truth about the functioning of the labor market and needs to be in any model of it. That phenomenon is right there in search-and-matching.

Quiggin makes much of the observation that the rise of Internet-based job searches has not led to a decline in the unemployment rate by making the search process more fluid, as the search-and-matching model supposedly predicts. But the issue is this: has the Internet actually changed how the labor market works? In some ways, it has. My organization, the Washington Center for Equitable Growth, currently has a job vacancy posted (one that would not be captured by the standard data on job vacancies) for which we’ve received a great many applications, whereas in the past a classified advertisement might have yielded a dozen phone calls and half that many mailed resumes.

But we will still take many weeks to interview candidates and fill the position. Thus, a decline in what might be considered search costs just leads to more searching, but not necessarily more matching. A similar dynamic is at play in the rise of the average number of colleges most applicants apply to: instead of streamlining the search process, more information just intensifies it.

There are other examples where one might have expected advances in information technology to have had a significant macroeconomic impact but which in fact have not. Financial integration is one: in the 1990s and early 2000s, then Federal Reserve Board chair Alan Greenspan assured us that in a world of instantaneous financial transactions and global credit markets, systemic risk could not rise because everyone is connected to everyone. We all saw how that turned out. Similarly, ATMs were supposed to have decreased the economy’s structural demand for money, which means that unless the money supply also shrank dramatically there would be high inflation. Nope. Exactly why supposedly world-changing technologies don’t actually change the world is a difficult question, but that critique is not one that pertains to search-and-matching labor market models specifically.

Quiggin also argues that the big question in labor market macroeconomics—essentially, why is labor demand low and why does it stay low—can only be answered by macroeconomic models. He asserts that search-and-matching models don’t add any insight. Let me offer an alternative schematization. There are two big questions in business cycle macroeconomics. Why do recessions happen? And why do they look the way they look, with high, persistent unemployment and a cascade of other symptoms of illness in the labor market?

Search-and-matching models don’t do anything on the first question; one has to assume the recession into the story. But the model goes a long way toward answering the second one if you allow for factual wage-bargaining and other modifications. In short, the model is a great tool to have in the economist’s toolbox, provided it’s used skillfully and with attention to the data, first and foremost.


July 15, 2014

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