Search for a theory of unemployment

The advantage of search theory is that it explicitly takes into account the frictions and the uncertainty that agents in the labour market face, and it allows us to understand unemployment as an equilibrium phenomenon

(pages 23-27 of printed journal)

By Ian King

Background

Unemployment has been one of the key issues in economics as a discipline and a central preoccupation of macroeconomics as a field. Indeed, many would argue that John Maynard Keynes (1936) invented macroeconomics to explain the soaring unemployment rates of the Great Depression. In this lecture, I'll review what I see as the main developments in the theory of unemployment, with a focus on modern theoretical developments and, in particular, 'search-theoretic' explanations. The aim is to identify what we have learned, and what remains to be explained.

Traditional explanations for unemployment

When seeking explanations for almost anything, an economist's first instinct is to think of supply and demand. Generically, for any good that is for sale, the quantity supplied increases with the price, and the quantity demanded decreases. The equilibrium price occurs where the demand and supply curves intersect. If the price is too high, then quantity supplied exceeds the quantity demanded, and the price falls towards the equilibrium price. Similarly, if the price is too low, then the quantity demanded exceeds the quantity supplied, and the price rises towards the equilibrium price. Applying this to the market for labour, unemployment is interpreted as a situation where the supply of labour exceeds its demand. Thus, when we see unemployment, the price of labour must be too high. What is the price of labour? Wages are the key component. However, in economies that experience variability in overall prices, it is important to keep in mind that it is real wages that matter: wages divided by prices. If we let W denote wages, in dollar terms, and P denote a price index, then the real wage is W/P. Thus, according to the standard model, if we see unemployment, it must mean that W/P is too high.

What, then, would reduce unemployment? According to this view, the problem can be solved by simply allowing the real wage W/P to fall, back to its equilibrium value. There are two channels through which this might occur: a fall in W or a rise in P. The relative importance of these two channels has been hotly debated by 'classical' and 'Keynesian' economists. In the 'classical' view, unemployment will naturally be reduced by a fall in the money wage W. The policy prescription, then, when faced with unemployment, is to simply wait for W to adjust downwards - which will inevitably occur, at least in the long run.

Keynes' most famous quotation is, of course: 'in the long run we are all dead.' In the context of the labour market, this quotation implies that it may take a long time before W adjusts to bring the real wage back down to its equilibrium level. Money wages can be 'sticky' downwards for a variety of reasons, and high levels of unemployment can therefore persist. In the Keynesian view, the government can fix the problem by somehow increasing P, rather than waiting for W to fall. P is the price of goods, which is determined in the goods market. This can be accomplished through aggregate demand management: either through expansionary fiscal or monetary policy, P will rise, W/P will fall, and full employment can be restored. The influence of Keynes' ideas was so profound that, for several decades, further developments in the theory of unemployment were mostly confined to answering the question: 'Why are wages sticky?'

Some inconvenient truths

These theories shed some light on unemployment, but they share some basic criticisms that reach to the heart of the basic supply-and-demand paradigm upon which their foundations lie. First and foremost, data on job vacancies has become available in recent years, and one of the key lessons from this data is that significant vacancy rates and unemployment rates can exist simultaneously. This is a problem for the standard model because, according to that model, unemployment is a symptom of W/P being too high, whereas unfilled vacancies are a symptom of W/P being too low. How can W/P be both too high and too low at the same time?

Secondly, data on wage dispersion has shown that significant dispersion exists, and has been growing over time - even for workers that, according to the data, share the same characteristics. The basic model predicts that there will be one wage (whether or not it is the equilibrium wage) in the market for each type of worker.

Clearly, a complete understanding of the causes of unemployment would require some explanation of these two basic facts. Search theory has risen, at least in part, to meet this challenge.

Search to the rescue

The basic idea in search theory is that workers actively search for jobs and/or firms actively search for workers, in an environment with uncertainty. This uncertainty can lead to the co-existence of both vacancies and unemployed workers and is consistent with wage dispersion. Search theory has its origins in the engineering literature, and early applications in economics were relatively straightforward adaptations - with physical variables reinterpreted as economic variables. Over the past few decades, though, search theory in economics has developed significantly so that several branches exist today.

Sequential search

The first branch of search theory in economics, introduced by McCall (1970) and Mortensen (1970), followed the engineering approach of Wald (1950) and is known as 'sequential search'. Here, each worker faces a set of possible job opportunities (vacancies) and knows properties about the distribution of wages available but does not know the specific wages available at individual vacancies. In order to find out the wages available at particular vacancies, the worker must visit the firm itself. This has a time cost: each visit takes one time period. The optimal strategy for a worker in this setting involves an 'optimal stopping rule': keep sampling (i.e. visiting firms) until she encounters a firm that is offering a wage above a certain reservation value - known as the 'reservation wage'. Once the worker is offered a wage above this value, the optimal rule says that she should accept that offer, and stop searching.

This branch of search theory has enjoyed a long history, and is still used today for modelling unemployment. It suffers, however, from a key criticism that was identified quite early on. The framework assumes that firms simply offer a different distribution of wages. In fact, as Rothschild (1973) pointed out, firm decisions are not modelled at all in this setting. Moreover, Diamond (1971) made the point that, if we try modelling firms' decisions in this setting, it becomes clear that firms would certainly not offer different wages. In fact, each firm would offer only the reservation wage. In that case, the entire distribution of wages degenerates down to only one wage, and no search would occur. This criticism has been a key driving force in the development of search theory ever since.

Equilibrium search

'Equilibrium search' originated in the work of Lucas and Prescott (1974). Here, the labour market is split up into a large number of distinct submarkets. Workers can participate in only one market at any time, but can choose to move from one market to another - with a cost of one time period. Lucas and Prescott interpret this movement as unemployment. In this setting, each location, with its own labour market, has competitive firms that face random shocks to their product demands - which imply random movements of the labour demand curves. In the absence of any aggregate uncertainty, in the steady state, in each time period a constant fraction of workers choose to move (i.e. be unemployed).

Lucas and Prescott left open the precise interpretation of what these locations would be. The most obvious interpretation is geography: physical locations such as cities or states. Another interpretation - which generated significant empirical investigation spearheaded by Lilien (1982) - is that each location represents a sector. (Thus, these are sometimes known as 'sectoral reallocation' models.) Yet another interpretation, one that I prefer myself, is that they represent professions. The common theme is that movement from one location to another is possible, but costly, for workers, and each location has uncertain productivity in the future.

Jovanovic (1987) pointed out a key criticism of this approach. If aggregate shocks (i.e. business cycles) are introduced into this setting, then worker movement turns out to be procyclical. This is problematic if this movement is interpreted as unemployment: it implies that there will be more unemployment in booms than in recessions! However, Jovanovic also proposed a fix-up: if workers have access to unemployment insurance, then some workers in low productivity locations will choose to 'rest' in their existing locations, waiting for local conditions to improve, while others will move. This, then, means that there are, conceptually, two types of unemployment in the model: 'search unemployment' and 'rest unemployment'. Jovanovic shows that rest unemployment is countercyclical and, under certain conditions, total unemployment is also countercyclical in this model. Jovanovic's original model allowed for only one worker per location, but similar results were found in models with competitive labour markets in each location (King (1990), Gouge and King (1997)).

In King and Sweetman (2002), we followed up the interpretation of each location as a profession, and considered the following question: is human capital re-tooling procyclical, as the theory implies? To answer this, we examined a data set which tracks the reasons for job separations, over several business cycles. One of the 13 possible reasons listed for job separations is 'return to school'. We considered this series for workers who were over the age of 25 (to rule out summer jobs) and found that it was profoundly procyclical - with approximately double the number of workers choosing to go back to school in booms rather than in recessions.

This approach to search certainly does have its advantages, but it does suffer from a major weakness: in all of these models, while workers can move, firms cannot. In fact, more generally, capital cannot move across locations in these models. This flies in the face of the reality of the world we live in, where capital mobility is a key feature. Incorporating capital decisions into this type of model is possible in principle but, so far, impossible in practice - due to the extreme technical complexity of these models. Introducing capital decisions, in effect, would require the fusion of two classic models developed by Lucas and Prescott: the equilibrium search model described above with the 'investment under uncertainty' model in Lucas and Prescott (1971). Despite the obvious appeal of taking this on, no-one has managed it yet.

Matching function search

Perhaps the simplest way to model the search process is to regard it as a technological, rather than economic one. This is the approach explored in papers by Diamond (1982), Mortensen (1982), and Pissarides (1985). In this setting, vacant jobs and unemployed workers are thought of as inputs to a technology which generates matches as its output. Workers and vacancies meet randomly and bilaterally (i.e. each vacancy will meet, at most, one worker, and vice versa), and then bargain over wages. Once again, job matches are also separated according to another random process and, in the steady state, the labour market experiences both unemployed workers and unfilled vacancies.

Arguably, this has become the dominant approach used to model unemployment in macroeconomics today. However, this approach does suffer from problems that arise from the purely technological nature of the matching process. First, due to the fact that prices (i.e. wages) play no role in the assignment of workers to vacancies, models of this sort have an inherent inefficiency built in. The equilibria of these models are generically inefficient, with efficiency only being obtained under miraculous circumstances when parameter values happen to be just right - the 'Hosios rule' (Hosios (1990)). Moreover, from the point of view of economic theory, this approach is somewhat disappointing because it abandons the project of analysing the economics of the search and matching process itself - leaving it as an exogenous process - and simply examines its implications.

Directed search

Directed search picks up exactly on this point. Here, workers and firms are modelled as being fully aware of each other's location, and of the wages available, but are uncoordinated in the sense that, when they choose who to approach, they are unaware of how many others are making the same choice. This can lead to situations where one vacancy may attract several workers, or vice versa. This congestion takes time to sort out and, with separation occurring at the other end, leads to both unemployed workers and unfilled vacancies in the steady state. In the tradition of modern game theory, this is typically modelled as a game, and the focus is on the mixed strategy equilibrium, where people choose probabilities of who to approach. This generates an equilibrium matching process which is very similar in nature to the matching function used in the approach described above, but which now embodies the conscious decisions of workers and firms.

This basic idea has been modelled in different ways. In Julien, Kennes, and King (2000), we modelled it with workers selling their labour, and firms choosing which workers to approach. In this setting, a worker may find that no-one approaches him, or one firm, or many - depending on the probabilities chosen by the firms, and the actual realisations. The wages paid to workers, in our framework, reflect how many firms approach the worker: effectively, the worker conducts an auction, with the highest bidder winning the right to employ the worker. If only one firm approaches the worker, then the wage is low: reflecting only the worker's outside options. However, if more than one firm approaches the worker, then the worker receives a premium that reflects the cost, to the firm, of waiting another period to hire a worker. This, therefore, induces wage dispersion in equilibrium.

Alternatively, Burdett, Shi, and Wright (2001) model directed search by having firms sell jobs to workers, where workers choose which firms to approach. In this setting, the firm may find different numbers of workers approaching, but always pay the same wage - no matter how many workers approach¹. In this case, no wage dispersion occurs in equilibrium.

In both cases, however, a fundamental trade-off exists for individuals when choosing who to approach: the person that offers the highest payoff will also be approached by the most people, so the probability of matching with that person is (relatively) small. If all sellers are identical, this leads to an outcome where all buyers assign the same probability to approaching each seller. However, if sellers are heterogeneous (i.e. some sellers have higher quality goods than others) then buyers will choose to assign higher probabilities to approaching higher quality sellers. In the context of the two different models described above, this implies that higher productivity workers will attract more firms, and higher productivity jobs will attract more workers.

Also, in both cases, when the labour market is large, the equilibrium outcome will be efficient in the sense that, given the coordination problem, the outcome maximises the expected amount of aggregate output. This makes these models quite different, from a policy perspective, from the matching function models discussed in the previous section. This also raises an interesting policy dilemma in models with heterogeneous workers: as mentioned above, in equilibrium, this implies that firms assign higher probability to approaching more productive workers. This is efficient, but it does not minimise the unemployment rate. Unemployment is minimised when firms assign equal probability to approaching each worker.

Directed search is now a burgeoning literature, with many new avenues being explored, of which I will mention only a few. Albrecht, Gautier, and Vroman (2006) develop a model that effectively synthesises the two directed search models mentioned above. In Julien, Kennes, and King (2006), we extend the basic model by allowing firms to create two different types of jobs: high and low quality ones, with higher quality ones being more expensive to create. Thus, the job mix becomes an endogenous variable, and the dispersion of wages becomes much more pronounced - closer, in calibrated examples, to the dispersion observed in empirical studies. In Julien, Kennes, King, and Mangin (2009), we introduce a public sector into the model, to examine the implications of tax rates, the progressivity of the tax structure, unemployment insurance, and employment subsidies in the basic model.

An assessment

Search has been used as a theory of unemployment for almost 40 years now. The advantage of search theory is that it explicitly takes into account the frictions and the uncertainty that agents in the labour market face, and it allows us to understand unemployment as an equilibrium phenomenon - rather than as a product of wages that, for some reason, are slow to fall. It can easily explain the co-existence of unemployed workers and unfilled vacancies, and provides us with some guidance about the efficiency of this process, and what the relevant trade-offs are from a policy perspective. From this point of view, search theory can be seen as having been quite successful.

Theoretically, with the recent development of search-theoretic models of the money market, it is now possible to build models with both unemployment and inflation as equilibrium phenomena (Berentsen, Menzio, and Wright (2008)). This allows for analysis of equilibrium Phillips curves, with solid microeconomic foundations. While current models of this sort allow for only random matching search, monetary models with directed search do exist (Julien, Kennes, and King (2008); Dutu, Julien, and King (2009)) and there is good reason to hope that directed search can shed light on these important macroeconomic issues. Despite its history, much work remains to be done in search theory.

Fundamentally, search theory is an expression of how to proceed optimally under circumstances that involve uncertainty. As Professor Nilss Olekalns mentioned in his inaugural lecture (Olekalns (2008)), for better or for worse, this is an inherent feature of the world we live in.

¹ See Shimer (1999) for an alternative approach, where firms auction off jobs.

References

Albrecht, J., P. Gautier, and S. Vroman, (2006) "Equilibrium Directed Search with Multiple Applications", Review of Economic Studies, 73, 869-891.

Berentsen, A., G. Menzio, and R. Wright, (2008) "Inflation and Unemployment in the Long Run", NBER Working Paper #13924

Burdett, K., S. Shi, and R. Wright (2001) "Pricing and Matching with Frictions", Journal of Political Economy, 109, 1060-1085.

Diamond, P., (1971) "A Model of Price Adjustment", Journal of Economic Theory, 3, 156-168.

Diamond, P., (1982) "Wage Determination and Efficiency in Search Equilibrium", Review of Economic Studies, 49, 217-229., 49, 217-229.

Dutu, R., B. Julien, and I. King, (2009) "Liquidity Constrained Competing Auctions", University of Melbourne Working Paper #1068.

Gouge, R., and I. King, (1997) "A Competitive Theory of Employment Dynamics", Review of Economic Studies, 64, 1-22., 64, 1-22.

Hosios, A., (1990) "On the Efficiency of Matching and Related Models of Search and Unemployment", Review of Economic Studies, 57, 279-298.

Jovanovic, B., (1987) "Work, Rest, and Search: Unemployment, Turnover, and the Cycle", Journal of Labor Economics, 5, 131-148.

Julien, B., J. Kennes, and I. King, (2000) "Bidding for Labor", Review of Economic Dynamics, 3, 619-649.

Julien, B., J. Kennes, and I. King, (2006) "Residual Wage Disparity and Coordination Unemployment", International Economic Review, 47, 949-978.

Julien, B., J. Kennes, and I. King, (2008) "Bidding for Money", Journal of Economic Theory, 142, 196-217.

Julien, B., J. Kennes, I. King, and S. Mangin (2009) "Directed Search, Unemployment, and Public Policy", Canadian Journal of Economics, (forthcoming)

Keynes, J. M., (1936) The General Theory of Employment, Interest, and Money, Reprinted Harcourt, Brace Jovanovich, New York.

King, I., (1990) "A Natural Rate Model of Frictional and Long-Term Unemployment", Canadian Journal of Economics, 23, 523-545.

King, I., and A. Sweetman (2002) "Procyclical Skill Retooling and Equilibrium Search" Review of Economic Dynamics, 5, 704-717.

Lilien, D., (1982) "Sectoral Shifts and Cyclical Unemployment", Journal of Political Economy, 90, 777-793.

Lucas, R., and E. Prescott (1971) "Investment under Uncertainty", Econometrica, 39, 659-681

Lucas, R., and E. Prescott (1974) "Equilibrium Search and Unemployment", Journal of Economic Theory, 7, 188-209.

McCall, J., (1970) "Economics of Information and Job Search", Quarterly Journal of Economics, 84, 113-126.

Mortensen, D., (1970) "A Theory of Wage and Employment Dynamics", in Phelps, E.(ed.) Microeconomic Foundations of Employment and Inflation Theory, Norton, New York.

Mortensen, D., (1982) "The Matching Process as a Noncooperative/Bargaining Game" in J.J. McCall (ed.), The Economics of Information and Uncertainty, 233-254, University of Chicago Press, Chicago.

Olekalns, N., (2008) "Policymaking in an Uncertain World", Insights, 3, 3-7.

Pissarides, C., (1985) "Short-Run Equilibrium Dynamics of Unemployment, Vacancies, and Real Wages", American Economic Review, 75, 676-690.

Rothschild, M., (1973) "Models of Market Organization with Imperfect Information: A Survey", Journal of Political Economy, 81, 1283-1308.

Shimer, R., (1999) "Job Auctions", Princeton University manuscript.

Wald, A., (1950) Statistical Decision Functions, John Wiley & Sons, New York.

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A condensed version of his Inaugural Lecture given at the University of Melbourne on 2 June 2009.

Professor Ian King is Professor of Economics and Director of the Centre for Macroeconomics and the University of Melbourne.

Volume 6 NOV 2009