A guide to directed search

Directed search: Matching partners with pricing data

Randall Wright, Philipp Kircher, Benoit Julien, Veronica Guerrieri 07 January 2018

Search models have vastly improved our knowledge of important market events that aren’t explained by classical economic theory, however they have a tendency to treat price formation as an afterthought. This column introduces a survey of the literature on ‘directed search’, which aims to keep carefully the explanatory power of search models but permits a meaningful role of prices in determining where people visit a trading partner.

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Search models have already been instrumental in understanding market phenomena that are hard to reconcile in classical economic theory, including the coexistence of unemployment and vacancies, price or wage dispersion and stickiness, bid-ask spreads, the down sides of bilateral trade that generate a job for the money and related institutions, partnership formation, and long and variable durations in enough time to execute trades in labour, housing, and other markets. Models in the celebrated Diamond-Mortensen-Pissarides tradition of random search give a unifying explanation for most of the facts. Yet within their endeavour they have a tendency to strip away an integral guiding force from classical models, namely, the purchase price. In particular, they have a tendency to treat price formation as an afterthought which has to be sorted out once agents meet (usually through bargaining) but that can’t be used to steer individuals’ search decisions. Because the price will not guide the meeting process, efficiency isn’t obtained except under very special conditions.

What will be an alternative way to take into account the result of prices and wages in shaping just how agents seek out trading partners? The fast-growing literature on ‘directed search’ aims to keep carefully the explanatory power of search models, but permits a meaningful role of prices in determining where people visit a trading partner. For instance, in the labour market an increased wage is assumed to attract more applicants typically, and decreases enough time a firm must fill its vacancy, however in contrast to classical models it generally does not reduce it to zero. Rather, more generous offers are associated with a higher possibility of trading, so they price the waiting time. Due to need for prices these models tend to be also known as competitive search models. This literature has its origins in simple IO models as in Peters (1984, 1991) and Burdett et al. (2001) and macro models as in Moen (1997) and Acemoglu and Shimer (1999), but has already reached out to numerous branches of micro and macro including diverse topics such as for example competitive posting of auctions, on-the-job search, or monetary theory and trade in asset markets. The purpose of our survey in Wright et al.(2017) is to examine, consolidate, and extend the literature upon this topic.

Competitive search bundles two characteristics: the terms of trade are posted by agents before meetings, and these terms direct search and therefore help determine who meets whom. In accordance with random search, this is simply not only a different philosophical method of the analysis of markets, however the mix of posting and directed search also alters substantive findings. Specifically, posted prices give agents incentives to search out particular counterparties. This often leads to advertise efficiency (it really is sometimes said the models internalise search externalities). Moreover, they dispense with the most common need for yet another parameter that determines the bargaining weights of both sides of the marketplace – the amount of transfers is chosen strategically in the model to balance the expenses with the advantages of quicker and/or better matches. A few of the models, however, not all, avoid the necessity for assuming a matching function as a result of micro-foundations of the actual search behaviour. Finally, the idea is tractable, often delivers cleaner results than alternatives, and bridges gaps between traditional search, general equilibrium, and game theory.

As a stylised preview of the primary mechanism that underlies these models, consider the easiest setting with homogeneous buyers and sellers (in the labour market analogue firms will be the buyers of labour and workers will be the sellers). If trade occurs at price p, buyers get yourself a utility of just one 1 without the price p, and buyers obtain utility p. No trade leads to zero utility. At different prices, different queues n(p) of buyers and sellers arise. A matching function determines the probability α that seller trades with a buyer, which is increasing in the buyer-seller ratio n(p) that’s formed at price p. So, their expected utility is α times p. Since α is increasing in the buyer-seller ratio, this is often represented as indifference curves over (p,n) pairs, as shown in Figure 1, where in fact the great things about longer queues of buyers are offset by higher prices. Higher utility is connected with higher curves. If a seller offers an increased price he changes the queue length and affects the likelihood of trade.

Figure 1 Indifference curves over (p,n)

Just how much does he affect the queue? Buyers’ expected utility includes increases in size from trade 1-p times their trading probability, which is decreasing in the queue of other buyers n. In equilibrium this expected utility takes some value U, that can be considered an indifference curve over (p,n) pairs for the customer. Figure 1 illustrates this indifference curve, where higher prices are compensated for by shorter queues for the nice. Sellers select a price-queue pair upon this curve to bring them with their highest indifferent curve, yielding equilibrium point (p*,n*). This Edgware-Box representation highlights the competitive part of the search models – agents value two margins (price and trading probability), and the costs aim to balance not only the purchase of the products but also the trading probabilities. The marketplace reaches a spot of efficiency regardless of the trading frictions. Because of this outcome, no matter which side posts the purchase price provided that the matching function remains unchanged.

Our survey reviews the idea more generally, with examples both in static economies in addition to with repeat purchases in labour, housing, or goods markets and in monetary economics. It aims to supply enough of the mathematical setup to permit novices an entrance into this growing literature, while providing depth and a wide review for individuals who already are somewhat familiar. In addition, it reviews the micro-foundations that underlie the insights just described by means of finite games, shows the way to handle heterogeneity and larger contracts spaces beyond simply posting prices, presents existing evidence about the directedness of search, and keeps an eye on economic applications.

References

Acemoglu, D, and R Shimer (1999), “Holdups and Efficiency with Search Frictions,” International Economic Review, 40, 827-850.

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

Moen, E R (1997), “Competitive Search Equilibrium,” Journal of Political Economy 105, 385-411.

Peters, M (1984), “Bertrand Equilibrium with Capacity Constraints and Restricted Mobility,” Econometrica 52, 1117-1128.

Peters, M (1991) “Ex Ante Price Offers in Matching Games: Non-Steady States,” Econometrica 59, 1425-1454.

Wright, R, P Kircher, B Julien and V Guerrieri (2017), “Directed Search – A Guided Tour”, NBER working paper 23884.

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