Ariel Pakes

What Really Matters in Designing School Choice Mechanisms

In the last decade, numerous student assignment systems have been redesigned using input from economists in the large American cities and elsewhere. This article reviews some of these case studies and uses practical experiences to take stock on what has really mattered in school choice mechanism design so far. While some algorithm design details are important, many are less practically important than initially thought. What really matters are basic issues that market operators in other contexts would likely be concerned about: straightforward incentives, transparency, avoiding inefficiency through coordination and well-functioning aftermarkets, and influencing inputs to the design, such as applicant decision-making and the quality of schools. INTRODUCTION In recent years, there has been a great deal of research activity and excitement among economists who study the design of systems used to assign students to schools. Motivated by Turkish college admissions, Balinski and Sonmez (1999) first defined the student placement problem, and Abdulkadiroglu and Sonmez (2003) defined the closely related school choice problem, motivated by K-12 public school admissions in the United States. Both articles showed how insights from matching theory could be used to re-engineer and potentially improve existing centralized school assignment systems. Abdulkadiroglu and Sonmez (2003) proposed two alternativemechanisms, which are adaptations of widely studied mechanisms in the literature on matching and assignment markets, following seminal contributions by Gale and Shapley (1962) and Shapley and Scarf (1974). Since that article was published, I have been involved in a number of efforts to redesign school choice systems, including those in New York City (2003), Boston (2005), New Orleans (2012), Denver (2012), Washington DC (2013), and Newark (2014). New systems have also been developed in England, Amsterdam, a number of Asian cities, and elsewhere. The purpose of this article is to review some facts from the field about these redesign efforts and to take stock on what I think has been important in practice so far. This article is not a survey of research on school choice market design (for surveys see, e.g., Pathak, 2011 and Abdulkadiroglu and Sonmez, 2013). My inspiration comes from Klemperer (2002), who presents his views on what matters for practical auction design based on his experience in designing auctions and advising bidders. Klemperer concludes that “in short, good auction design is mostly good elementary economics,” whereas “most of the extensive auction literature is of second-order importance for practical auction design.”

Learning, Experimentation, and Information Design

INTRODUCTION The purpose of this paper is to survey recent developments in a literature that combines ideas from experimentation, learning, and strategic interactions. Because this literature is multifaceted, let us start by circumscribing our overview. First and foremost, all surveyed papers involve nontrivial dynamics. Second, we will restrict attention to models that deal with uncertainty. Models of pure moral hazard, in particular, will not be covered. Third, we exclude papers that focus on monetary transfers. Our goal is to understand incentives via other channels – information in particular, but also delegation. Fourth, we focus on strategic and agency problems, and so leave out papers whose scope is decision-theoretic. However, rules are there to be broken, and we will briefly discuss some papers that deal with one-player problems, to the extent that they are closely related to the issues at hand. Finally, we restrict attention to papers that are relatively recent (specifically, we have chosen to start with Bolton and Harris, 1999). Our survey is divided as follows. First, we start with models of strategic experimentation. These are abstract models with few direct economic applications, but they develop ideas and techniques that percolate through the literature. In these models, players are (usually) symmetric and externalities are (mostly) informational. Moving beyond the exploitation/exploration trade-off, we then turn to agency models that introduce a third dimension: motivation. Experimentation must be incentivized. The first way this can be done (Section 3) is via the information that is being disclosed to the agent performing the experimentation, by a principal who knows more or sees more. A second way this can be done is via control. The nascent literature on delegation in dynamic environments is the subject of Section 4. Section 5 turns to models in which information disclosure is not simply about inducing experimentation, but manipulating the agents action in broader contexts. To abstract from experimentation altogether, we assume that the principal knows all there is to know, so that only the agent faces uncertainty. Finally, Section 6 discusses experimentation with more than two arms (Callander, 2011). EQUILIBRIUM INTERACTIONS Strategic Bandits Strategic bandit models are game-theoretic versions of standard bandit models. While the standard “multi-armed bandit” describes a hypothetical experiment in which a player faces several slot machines (“one-armed bandits”) with potentially different expected payouts, a strategic bandit involves several players facing (usually, identical) copies of the same slot machine.

Dynamic Selection and Reclassification Risk: Theory and Empirics

This chapter surveys the theory and evidence on contracting under learning and imperfect commitment.We present a simple model of long-term insurance a la Harris and Holmstrom (1982) to show the relevance and insights of the theory. Different variations of the model encompass many situations that have been studied in diverse areas of Economics, including Labor, Finance, and Insurance. The model is useful for understanding issues such as dynamic selection and reclassification risk. Imperfect commitment is shown to be the source of adverse selection and partial insurance in environments with learning, even when information is symmetric. The empirical literature has looked at the testable implications regarding selection and optimal contracts. Recent work has focused on the welfare loss from lack of commitment, which has been found to be substantial. The theory offers policy prescriptions on how to contend with the market distortions associated with limited commitment. INTRODUCTION The provision of insurance is one of the main determinants of how societies organize and regulate economic activity. Since insurance may create perverse incentives, different economic systems – and forms of capitalism – represent distinct alternatives over such trade-offs. The provision of longterm insurance requires commitment to prevent the exclusion of those with the most unfortunate realizations and maintain participation of the most fortunate. Such interactions between insurance provision, incentives, and commitment have been central to the contract theory literature since the 1980s. Economists have studied the provision of long-term insurance in the context of labor contracts (Harris and Holmstrom, 1982; Holmstrom, 1983), insurance markets (Pauly, Kunreuther and Hirth, 1995), consumption and savings (Hall, 1978), as well as development economics, where villagers who lack sophisticated financial instruments may rely on mutual insurance within the village (Townsend, 1994). These agency problems arise between firms and customers, firms and employees, or among firms. This chapter surveys the empirical literature on dynamic contracting. We focus on long-lasting relations between parties, in which the dynamics are driven by information revelation. Evolving information generates gains from long-term contracts to cope with reclassification risk. Reclassification risk is a concern in many markets, such as health or life insurance. The literature is useful for understanding insurance provision and market design.

Shocks, Sign Restrictions, and Identification

This chapter highlights some key issues in the use of sign restrictions for the purpose of identifying shocks. It does so by examining two benchmark examples. In the first part, I discuss a generic example of demand and supply, seeking to identify a supply shock from price–quantity data. In the second part, I discuss a generic example of Bayesian vector autoregressions and the identification of a monetary supply shock. Along the way, I formulate some principles and present my view on some of the recent discussion and literature regarding sign restrictions. INTRODUCTION The approach of sign restrictions in time series analysis has generated an active literature, many successful applications, and a lively debate. The procedures are increasingly easy to use, with implementations in econometric software packages such as RATS or with ready-to-implement code in a variety of programming languages; see, e.g., Danne (2015) as one example. Let me say from the outset that I am very happy about that, including those contributions that have criticized my own work, sometimes sharply. Skepticism and critique is crucial for science to advance, so all power to them! That should not prevent me from critiquing back, of course, and that is partly what this chapter will be about. Debate is good. While Leamer (1981) surely deserves being highlighted here, I believe that the literature pretty much started with Dwyer (1998), Faust (1998) and its discussion, Uhlig (1998), Canova and Pina (1999), Canova and de Nicolo (2002), as well as my “agnostic identification” paper Uhlig (2005b). This one was published quite a number of years after my discussion of the Faust paper, but that discussion shows that I had already developed my methodology then, and that imposing sign restrictions on impulse responses and not just on impact can add considerable bite. There are deep connections to the seemingly different literature on partial identification and estimation subject to inequality restrictions: rather than review that literature, let me just point the reader to the excellent discussions on this topic by Canay and Shaikh (2017) as well as by Ho and Rosen (2017), appearing elsewhere in this volume, or, say, Kline and Tamer (2016).

Networks in Economics: Remarks

The past fifteen years has seen a burst in research on the economics of networks. Researchers have been studying a wide range of economic settings, and in each case, links between individuals arguably play critical roles in individual and aggregate outcomes. The following are some examples, with specified settings and links: peer effects with friendship links, innovation/research and development with links between researchers and colleagues, local public goods with geographic and social links, oligopoly and firms’ interlinked markets, macroeconomic shocks and supply chain links, information transmission and people’s social links, banking and links due to crossholdings, and markets and links between buyers and sellers. The mathematical structure of networks ties together all this research. In a network, agents have pairwise “links” that affect their dealings. These links collectively give the “adjacency matrix,” also called the “graph,” or the “network,” that impacts outcomes for all agents. At the individual level, an agent’s payoffs depend directly on the actions of her “neighbors,” i.e., the agents to whom she is linked. Distant agents also shape payoffs and incentives to the extent they are indirectly linked, by “paths” in the network. These remarks give a bird’s eye of this research, providing a road map to bring together the detailed accounts of the empirical and theoretical research provided by the two papers in this session. Following the road map, these remarks give a whirlwind tour of research objectives and themes and present challenges for future studies. Research papers in this area typically begin with documenting an economic outcome of interest and recognizing that a network. underlies this outcome. Figure 1 gives a road map. Starting at the top, a theoretical study typically posits pairwise links between N agents that form a network G. An empirical study will also typically begin with data on the links that make up the network, i.e., who is linked to whom in the relevant population. There are then two black boxes to be filled in. The first box concerns how networks shape outcomes, i.e., the theory and empirics of how individual actions, given a network, lead to the economic outcome. The second black box concerns network formation, i.e., how links come about in the first place.

Recent Advances in Empirical Analysis of Financial Markets: Industrial Organization Meets Finance

In this article I provide a selective review of recent empirical work in the intersection of finance and industrial organization. I describe an estimation method, which can be applied quite widely in financial and other markets where a researcher needs to recover agents’ beliefs. Using four applications I illustrate how combining this method with data from auctions and with a theoretical model can be used to answer various economic questions of interest. I start with the primary market for sovereign debt, focusing on treasury bill auctions of the US and Canada. I show how auction data together with standard tools from Industrial Organization can be used to shed light on issues involving market structure, market power and front-running. I continue by looking at the Main Refinancing Operations of the European Central Bank, the main channel of monetary policy implementation in the EURO-zone, and illustrate how auction data can be used to learn about typically opaque over-the-counter lending markets. I also discuss how to use these data indirectly to learn about dynamics of banks’ financial health and of their balance sheets. I then turn to the discussion of recent progress on estimation of systemic risk. I finish with thoughts on how to estimate a whole demand system for financial assets. Thanks to Ali Hortaçsu for continued cooperation and to Ariel Pakes, Rob Porter, Azeem Shaikh and Moto Yogo for their comments. I am grateful for the financial support of the NSF (SES-1352305) and the Sloan Foundation. All remaining errors are mine. Department of Economics, Princeton University, NBER and CEPR

Discussion of “Agency Problems”

Apart from their high quality, these two papers share a common thread: they emphasize learning. Now learning can take place in a wide variety of ways. It can be a purposeful and costly activity; or information can flow in exogenously. One can learn from ones own experiments, as well as from observing others’ experimenting and its results; or learning can be informed by recommendations from experts. In a market situation, one can learn from competitors, in ways that are shaped both by their strategies and by regulations. Learning also builds on what one already knows; in modelling terms, some information about the world must be assumed to be known. I will return to this perhaps obvious point in my conclusion. In the models surveyed by Horner and Skrzypacz, learning is costly, as experimenting with a risky choice forgoes the benefits of safer options. In so far as each agent can also learn from what (s)he observes on other agents experiments, this opens the door to free riding. But since other agents’ payoffs to experimenting depend on their current beliefs, it is sometimes useful to experiment in order to change these beliefs – “nudging” others to experiment. This strategic interaction between agents in turn opens the door for other parties to attempt to manipulate information accrual. The seller of a new experience good, for instance, can design the way it rewards early adopters for their reviews, or simply how it chooses to publish them. Hendels chapter builds on a long tradition in contract theory: it has principals learning about agents’ types over time. The main focus of the chapter is on the case when each agents type changes exogenously over time, so that learning occurs on both sides of the relationship. Learning can still be asymmetric, both because the agent learns his type privately and/or because other principals may not observe what one principal has learnt. Unlike much of the theoretical literature on dynamic contracting, Hendel focuses on learning that is symmetric between the two parties in a relationship, but may be asymmetric between the various principals: my insurer learns my risk at the same time that I do, but her competitors may be equally well-informed (“symmetric learning” in the chapter) or not (“asymmetric learning”.) Given limited commitment, changes in the agents type may give rise to reclassification risk: insurers are tempted to index premia to risk.