Knowledge that Transforms

This article deals with the identification and estimation of dynamic games when players’ beliefs about other players’ actions are biased, that is, beliefs do not represent the probability distribution of the actual behaviour of other players conditional on the information available. First, we show that an exclusion restriction, typically used to identify empirical games, provides testable non-parametric restrictions of the null hypothesis of equilibrium beliefs in dynamic games with either finite or infinite horizon. We use this result to construct a simple Likelihood Ratio test of equilibrium beliefs. Second, we prove that this exclusion restriction, together with consistent estimates of beliefs at two points in the support of the variable involved in the exclusion restriction, is sufficient for non-parametric point-identification of players’ belief functions as well as useful functions of payoffs. Third, we propose a simple two-step estimation method. We illustrate our model and methods using both Monte Carlo experiments and an empirical application of a dynamic game of store location by retail chains. The key conditions for the identification of beliefs and payoffs in our application are the following: (1) the previous year’s network of stores of the competitor does not have a direct effect on the profit of a firm, but the firm’s own network of stores at previous year does affect its profit because the existence of sunk entry costs and economies of density in these costs; and (2) firms’ beliefs are unbiased in those markets that are close, in a geographic sense, to the opponent’s network of stores, though beliefs are unrestricted, and potentially biased, for unexplored markets which are farther away from the competitors’ network. Our estimates show significant evidence of biased beliefs. Furthermore, imposing the restriction of unbiased beliefs generates a substantial attenuation bias in the estimate of competition effects.

Bureaucracies are configured differently to private sector and political organizations. Across a wide range of civil services entry is competitive, promotion is constrained by seniority, jobs are for life and retirement occurs at a fixed age. This implies that older entering officers, who are less likely to attain the glittering prize of reaching the top of the bureaucracy before they retire, may be less motivated to exert effort. Using a nationwide stakeholder survey and rich administrative data on elite civil servants in India we provide evidence that: (i) officers who cannot reach the senior-most positions before they retire are perceived to be less effective and are more likely to be suspended and (ii) this effect is weakened by a reform that extends the retirement age. Together these results suggest that the career incentive of reaching the top of a public organization is a powerful determinant of bureaucrat performance.

We study the aggregation of dispersed information in elections in which turnout may depend on the state. State-dependent turnout may arise from the actions of a biased and informed “election organizer”. Voters are symmetric ex ante and prefer policy a in state α and policy b in state β, but the organizer prefers policy a regardless of the state. Each recruited voter observes a private signal about the unknown state but does not learn the turnout. First, we characterize how the outcomes of large elections depend on the turnout pattern across states. In contrast to existing results for large elections, there are equilibria in which information aggregation fails whenever there is an asymmetry in turnout; information aggregation is only guaranteed in all equilibria if turnout is state independent. Second, when the turnout is the result of costly voter recruitment by a biased organizer, the organizer can ensure that its favourite policy a is implemented with high probability independent of the state as the voter recruitment cost vanishes. Moreover, information aggregation will fail in all equilibria. The critical observation is that a vote is more likely to be pivotal for the decision if turnout is smaller, leading to a systematic bias of the decision toward the low-turnout state.

This article studies the optimal determination of bankruptcy exemptions for risk averse borrowers who use unsecured contracts but have the possibility of defaulting. In a large class of economies, knowledge of four variables is sufficient to determine whether a bankruptcy exemption level is optimal or should be increased or decreased. These variables are 1. the composition of households’ liabilities, 2. the sensitivity of the credit supply schedule to exemption changes, 3. the probability of filing for bankruptcy with non-exempt assets, and 4. the value given by households to a marginal dollar in different states, which can be mapped to changes in households’ consumption. I recover empirical estimates of the sufficient statistics using U.S. data over the period 2008–16 and find that increasing exemption levels improves overall welfare, although there is substantial variation in estimated welfare gains across U.S. states and income quintiles.

We study the relationship between homebuyers’ beliefs about future house price changes and their mortgage leverage choices. Whether more pessimistic homebuyers choose higher or lower leverage depends on their willingness and ability to reduce the size of their housing market investments. When households primarily maximize the levered return of their property investments, more pessimistic homebuyers reduce their leverage to purchase smaller houses. On the other hand, when considerations such as family size pin down the desired property size, pessimistic homebuyers reduce their financial exposure to the housing market by making smaller downpayments to buy similarly-sized homes. To determine which scenario better describes the data, we investigate the cross-sectional relationship between house price beliefs and mortgage leverage choices in the U.S. housing market. We use plausibly exogenous variation in house price beliefs to show that more pessimistic homebuyers make smaller downpayments and choose higher leverage, in particular in states where default costs are relatively low, as well as during periods when house prices are expected to fall on average. Our results highlight the important role of heterogeneous beliefs in explaining households’ financial decisions.

In markets where sellers are able to price discriminate, individuals pay different prices that may be unobserved by the econometrician. This article considers the structural estimation of a demand and supply model of differentiated products with such price discrimination and limited information on prices taking the form of, e.g., observing list prices from catalogues or average prices. Within this framework, identification is achieved not only with usual moment conditions on the demand side, but also through supply-side restrictions. The model can be estimated by GMM using a nested fixed point algorithm that extends the usual contraction mapping algorithm to our setting. We apply our methodology to estimate the demand and supply in the French new automobile market. Our results suggest that discounting arising from price discrimination is important. The average discount is estimated to be 9.6%, with large variation depending on buyers’ characteristics and cars’ specifications. Our results are consistent with other evidence on transaction prices in France.

We study two wage bargaining games between a firm and multiple workers. We revisit the bargaining game proposed by Stole and Zwiebel. We show that, in the unique Subgame Perfect Equilibrium, the gains from trade captured by workers who bargain earlier with the firm are larger than those captured by workers who bargain later, as well as larger than those captured by the firm. The resulting equilibrium payoffs are different from those reported in Stole and Zwiebel as they are not the Shapley values. We propose a novel bargaining game, the Rolodex game, which follows a simple and realistic protocol. In the unique no-delay Subgame Perfect Equilibrium of this game, the payoffs to the firm and to the workers are their Shapley values.

The world’s poor are seeing a rapid expansion in access to formal savings accounts. What is the source of savings when households are connected to a formal account? We combine a high-frequency panel survey spanning two and a half years with an experiment in which a Sri Lankan bank used mobile Point-of-Service (POS) terminals to collect deposits directly from households each week. We find that the headwaters of formal savings lie in sacrificed leisure time: households work more, and improved savings options generate an increase in labour effort in both self-employment and in the wage market. The results suggest that the labour allocation channel is an important mechanism linking savings opportunities to income.

We model and test two school-based peer cultures: one that stigmatizes effort and one that rewards ability. The model shows that either may reduce participation in educational activities when peers can observe participation and performance. We design a field experiment that allows us to test for, and differentiate between, these two concerns. We find that peer pressure reduces takeup of an SAT prep package virtually identically across two very different high school settings. However, the effects arise from very distinct mechanisms: a desire to hide effort in one setting and a desire to hide low ability in the other.

This article investigates how the success of a management practice depends on the underlying values articulated by the management. A large U.S. transportation company is in the process of fitting its trucks with an electronic on-board recorder (EOBR) to provide drivers with information on their driving performance. The company also has commenced a multi-year initiative to remake its internal operations, the first phase of which focuses exclusively on changing values toward a greater emphasis on teamwork and empowerment. In this setting, a natural question is whether the optimal managerial practice consists of: (1) letting each driver know his or her individual performance only; or also (2) providing drivers with information about their performance with respect to other drivers. Using the EOBR-provided driver performance data, we randomize these practices across sites. The main result of our experiment is that (2) leads to better performance than (1) in a particular site if and only if the site has not yet received the values intervention, and worse performance if it has. The result is consistent with the presence of a conflict between competition-based managerial practices and a shift to a cooperation-based value system. More broadly, it highlights the role of intangible factors in determining the optimal set of managerial practices.