Working papers results

We relate two representations of the cost of acquiring information: a cost that depends on the experiment performed, as in statistical decision theory, and a cost that depends on the distribution of posterior beliefs, as in the theory of rational inattention. In many cases of interests, the two representations prove to be inconsistent with each other. We provide a systematic analysis of the inconsistency, propose a way around it, and apply our findings to information acquisition in games.

We add here another layer to the literature on nonatomic anonymous games started with the 1973 paper by Schmeidler. More specifically, we define a new notion of equilibrium which we call '-estimated equilibrium and prove its existence for any positive '. This notion encompasses and brings to nonatomic games recent concepts of equilibrium such as self-confirming, peer-confirming, and Berk-Nash. This augmented scope is our main motivation. At the same time, our approach also resolves some conceptual problems present in Schmeidler (1973), pointed out by Shapley. In that paper the existence of pure-strategy Nash equilibria has been proved for any nonatomic game with a continuum of players, endowed with an atomless countably additive probability. But, requiring Borel measurability of strategy profiles may impose some limitation on players' choices and introduce an exogenous dependence among players' actions, which clashes with the nature of noncooperative game theory. Our suggested solution is to consider every suset of players as measurable. This leads to a nontrivial purely finitely additive component which might prevent the existence of equilibria and requires a novel mathematical approach to prove the existence of '-equilibria.

The allocation of bureaucrats across tasks constitutes a pivotal instrument for achieving an organization's objectives. In this paper, I measure the performance of World Bank bureaucrats by combining the universe of task assignment with an evaluation of task outcome and a hand-collected dataset of bureaucrat CVs. I introduce two novel stylized facts. First, bureaucrat performance correlates with task features and individual characteristics. Second, there exists a negative assortative matching between high-performing bureaucrats and low-performing countries. In the aftermath of natural disasters, which may weaken countries' performance even further, I observe that low-performing countries receive an additional allocation of high-performing bureaucrats. I discuss various interpretations of these findings.

We show that the incentive to engage in exclusionary tying (of two complementary products) may arise even when tying cannot be used as a defensive strategy to protect the incumbent's dominant position in the primary market. By engaging in tying, an incumbent firm sacrifices current profits but can exclude a more efficient rival from a complementary market by depriving it of the critical scale it needs to be successful. In turn, exclusion in the complementary market allows the incumbent to be in a favorable position when a more efficient rival will enter the primary market, and to appropriate some of the rival's efficiency rents. The paper also shows that tying is a more profitable exclusionary strategy than pure bundling, and that exclusion is the less likely the higher the proportion of consumers who multi-home.

We report on a laboratory experiment measuring the preferences of a unique pool of risk professionals over various sources of uncertainty that entail different degrees of complexity. We then compare these preferences with those of a control group composed of social science students to obtain a deeper understanding of the mechanisms driving behaviors under risk and ambiguity. We find that (1) ambiguity aversion is robust to subjects' degree of sophistication in probabilistic reasoning and background. (2) An association exists between attitudes toward ambiguity and compound risk for students/less sophisticated subjects, and is mainly explained by their attitudes toward complexity. Such an association does not exist for risk professionals/more sophisticated subjects. (3) The failure to reduce compound risk emerges as a sufficent, but not necessary, condition for ambiguity non-neutrality. These findings suggest that decision making under ambiguity cannot be reduced to decision making under risk.

Two extensive game structures with imperfect information are said to be behaviorally equivalent if they share the same map (up to relabelings) from profiles of structurally reduced strategies to induced terminal paths. We show that this is the case if and only if one can be transformed into the other through a composition of two elementary transformations, commonly known as "Interchanging of Simultaneous Moves" and "Coalescing Moves/Sequential Agent Splitting."

This paper proposes a new approach to factor modeling based on the long-run equilibrium relation between prices and related drivers of risk (integrated factors). We show that such relationship reveals an omitted variable in standard factor models for returns that we label as Equilibrium Correction Term (ECT). Omission of this term implies misspecification of every factor model for which the equilibrium (cointegrating) relation holds. The existence of this term implies short-run mispricing that disappears in the long-run. Such evidence of persistent but stationary idiosyncratic risk in prices is consistent with deviations from rational expectations. Its inclusion in a traditional factor model improves remarkably the performance of the model along several dimensions. Furthermore, the ECT -being predictive- has strong implications for risk measurement and portfolio allocation. A zero-cost investment strategy that consistently exploits temporary idiosyncratic mispricing earns an average annual excess return of 6.21%, mostly unspanned by existing factors.

This paper presents a model of selective exposure to information and an experiment to test its predictions. An agent interested in learning about an uncertain state of the world can acquire information from one of two sources which have opposite biases: when informed on the state, they report it truthfully; when uninformed, they report their favorite state. When sources have the same reliability, a Bayesian agent is better off seeking confirmatory information. On the other hand, it is optimal to seek contradictory information if and only if the source biased against the prior is sufficiently more reliable. We test these predictions with an online experiment. When sources are symmetrically reliable, subjects are more likely to seek confirmatory information but they listen to the other side too frequently. When sources are asymmetrically reliable, subjects are more likely to consult the more reliable source even when prior beliefs are strongly unbalanced and listening to the less reliable source is more informative. Moreover, subjects follow contradictory advice sub-optimally; are too trusting of information in line with a source bias; and too skeptic of information misaligned with a source bias. Our experiment suggests that biases in information processing and simple heuristics - e.g., listen to the more reliable source - are important drivers of the endogenous acquisition of information.

MIn many domains, committees bargain over a sequence of policies and a policy remains in effect until a new agreement is reached. In this paper, I argue that, in order to assess the consequences of veto power, it is important to take into account this dynamic aspect. I analyze an infinitely repeated divide-the-dollar game with an endogenous status quo policy. I show that, irrespective of legislators' patience and the initial division of resources, policy eventually gets arbitrarily close to full appropriation bythe veto player; that increasing legislators' patience or decreasing the veto player's ability to set the agenda makes convergence to this outcome slower; and that the veto player supports reforms that decrease his allocation. These results stand in sharp contrast to the properties of models where committees bargain over a single policy. The main predictions of the theory find support in controlled laboratory experiments.

Here we report the results of a large RCT conducted at the pan-African level that wants to shed light on the impact of peer effects on innovation and entrepreneurship. The experiment involved around 5000 entrepreneurs (some established, other just aspiring) from 49 African countries. All of those entrepreneurs completed an online business course, while only the treated ones had the additional possibility of interacting with peers, within groups of sixty, and in one of three different setups: (a) face-to-face, (b) virtually 'within' (where interaction was conducted through an Internet platform in groups of entrepreneurs of the same country), (c) virtually 'across' (where the virtually connected groups displayed a balanced heterogeneity across countries). After two and a half months, all participants were asked to submit business proposals. The ones submitted were then evaluated in a two-stage procedure. First, they were graded by a panel of African professionals; subsequently, the pool of highest-graded proposals were again assessed and graded by senior investors, who selected some for possible funding. Two outcome variables follow from this evaluation exercise: the (optional) decision of whether to submit a proposal, and the grades (1 to 5) obtained by the proposals that were submitted. Next, we outline our main results concerning the effect of the treatment on the two aforementioned outcomes - submission and quality (measured in the intensive margin) - as well as the combination of both of them that we call, for short, extensive quality. (1) Virtual-within interaction has a positive and significant treatment effect on the three dimensions: submission, intensive quality, and extensive quality. Instead, when interaction is face-to-face (thus also "within') only submission and the extensive quality margin are affected (positively so). (2) Virtual-across interaction yields no significant effect on any of the former three dimensions. (3)When effective on quality (cf. (1)), the treatment operates by shifting up, on average the evaluation grade of business proposals from low levels (grades 1 or 2) to high ones (grades 4 or 5). (4) The baseline quality of entrepreneurs has a positive effect on performance. However, the average such quality of the peers in one's own group has a negative composition effect on intensive quality. In fact, a similarly negative effect is also induced by peers' average experience level. (5) As a robustness test, the core treatment effects described in (1)-(2) are confirmed to remain essentially unchanged under a full range of control (baseline) variables, while the composition effects identified in (4) are found to survive a standard placebo test. As a second step in the analysis, we construct a social network in each group by defining the weigh of a directed link between two entrepreneurs as the amount of information (overall size of messages) written by one of them for which there is evidence that the other has been exposed to, then writing a subsequent message. Then, on the basis of the network structure so defined, we estimate the induced peer effects and arrive at the following conclusions. (6) In large countries (the only ones for which a sufficient number homogeneous groups can be formed), virtual-within interaction leads to positive and significant peer effects on submission and extensive quality, but not intensive quality. Instead, when entrepreneurs of large countries are exposed to virtual-across interaction, no significant peer effects arise in any of the three outcomes. (7) In the set of small countries, where only virtual-across interaction is possible, there are positive and significant peer effects on both extensive and intensive quality but not on submission. (8) Composition effects on network peers are weak, largely captured by (outcome-based) peer effects. (9) Results (6)-(7) are structurally robust to redefining the network links in the following two ways: (a) they are limited to involve less than a maximum communication lag, suitably parametrized; (b) they are two-sided, their weight tailored to the flow information channeled in both directions. A combined consideration of (1)-(9) reveals an interesting contrast between treatment and peer effects. For example, in view of (1)-(3), we may conclude that whereas some group homogeneity - or face-to-face contact - bring about positive treatment effects, the group heterogeneity induced by virtual-across interaction fails to deliver significant such effects on all three dimensions. Instead, (6)-(7) indicate that network-based peer effects deliver an intriguingly different pattern. For, under virtual-within interaction, we find that entrepreneurs' peers exert a significantly positive influence on submission (and the extensive margin) but not so on quality per se (in the intensive margin, while a some what polar behavior arises in small countries who undergo virtual-across interaction. This suggests that whereas homogeneity leads to peer interaction that is rather independent of peer performance, heterogeneity has peer performance play an important role (both in positive or negative terms, depending on the quality of that performance). Overall, this induces an effect of the treatment that is significantly positive under homogeneity (virtual-within interaction for large countries) but not strong enough to be significant under full-fledged heterogeneity (virtual-across interaction for small countries). The aforementioned contrast between the nature and implications of the treatment effects stated in (1)-(4) and the network peer effects in (6)-(8) is interesting and deserves further investigation. A possible explanation for it might hinge upon the positive role that homogeneity/familiarity may play as a source of encouragement (and hence participation), as opposed to the negative impact it could have in reducing the novelty of ideas and/or highlighting the fear of competition (thus dis-incentivizing information sharing and thus a genuine effect induced by peer performance). To gain a good understanding of these issues, however, one needs the help of theory as well as a detailed investigation of how communication actually unfolds in our context. Both lines of work are part of our ongoing research. Here, we provide a preliminary account of the latter, which is included in the final part of the paper. Our approach to semantic analysis relies on the machine-learning tools developed by the modern field of Natural Language Processing (NLP). This methodology is applied to the vast flow of information exchanged by entrepreneurs (over 140,000 messages) in order to identify, first, what have been the modes/categories of peer communication more prevalent in our context, e.g. business focus, sentiment/encouragement, target audience, etc. Then we use this information to understand what are the different patterns of communication most prevalent in our context, as captured by a corresponding set of conditional and unconditional distributions that show and how communication is associated to: (a)endogenous variables such as behavior or performance; (b)exogenous variables, such as treatment type or individual baseline characteristics. The main conclusions obtained so far can be summarized as follows. Messages are quite polarized in either the business or sentiment dimension, showing an inverse dependence in the (strong) FOSD sense between the respective distributions. Applying the same comparison criterion, we also find that highly performing agents use more business-focused messages, which are not only neutral in sentiment but also targeted to specific peers (rather than being general messages). Interestingly, however, the treatment arm (virtual-within or -across) has no significant effect on the type of communication, while baseline quality and a measure of "motivation' do have an effect analogous to that described before for performance. Finally, we also rely on the message categorization induced by the NLP analysis to construct semantically weighted networks on two specific features/categories: business relevance and sentiment. Quite remarkably, the corresponding peer effects are found to be unaffected by either of these "semantic projections' of the social network. This suggests that, even though entrepreneurs' messages focus heavily on business issues, their communication displays a feature that is often observed in ordinary (non-virtual) interaction: there is a balance between business focus and a comparable amount of sentiment-laden talk.