Working papers results

Many separable dynamic incentive problems have primal recursive formulations in which utility promises serve as state variables. We associate families of dual recursive problems with these by selectively dualizing constraints. We make transparent the connections between recursive primal and dual approaches, relate value iteration under each and give conditions for it to be convergent to the true value function.

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In real-life elections, vote-counting is often imperfect. We analyze the consequences of such imperfections in plurality and runoff rule voting games. We call a strategy profile a robust equilibrium if it is an equilibrium if the probability of a miscount is positive but small.

All robust equilibria of plurality voting games satisfy Duverger's Law: In any robust equilibrium, exactly two candidates receive a positive number of votes. Moreover, robust- ness (only) rules out a victory of the Condorcet loser.

All robust equilibria under runoff rule satisfy Duverger's Hypothesis: First round votes vare (almost always) dispersed over more than two alternatives. Robustness has strong implications for equilibrium outcomes under runoff rule: For large parts of the parameter space, the robust equilibrium outcome is unique.

This is a survey of some of the recent decision-theoretic literature involving beliefs that cannot be quantified by a Bayesian prior. We discuss historical, philosophical, and axiomatic foundations of the Bayesian model, as well as of several alternative models recently proposed. The definition and comparison of ambiguity aversion and the updating of non-Bayesian beliefs are briefly discussed. Finally, several applications are mentioned to illustrate the way that ambiguity (or "Knightian uncertainty") can change the way we think about economic problems.

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The available empirical evidence suggests that the distribution of income and its composition play an important role in explaining tax noncompliance. We address the issue from a macroeconomic point of view, building a dynamic general equilibrium Bewley- Huggett-Aiyagari model that jointly endogenizes tax evasion and income heterogeneity. Our results showthat the model can successfully replicate the salient qualitative and quantitative features of U.S. data. In particular, the model replicates fairly well the shape of the cross-sectional distribution of misreporting rates over true income levels. Furthermore, we show that a switch from progressive to proportional taxation has important quantitative effects on noncompliance rates and tax revenues.

This article compares the impact of plague across Europe during the seventeenth century. It shows that, contrary to received wisdom, seventeenth century plague cannot be considered a "great equalizer": the disease affected southern Europe much more severely than the north. In particular, Italy was by far the area worst struck. Using both archival sources and previously published data, the article introduces a novel epidemiological variable that has not been considered in the literature: territorial pervasiveness of the contagion. This variable is much more relevant than local mortality rates in accounting for the different regional impact of plague. The article shows that pandemics, and not economic hardship, generated a severe demographic crisis in Italy during the seventeenth century --- at a time when northern European populations were growing quickly. Plague caused a "system shock" to the economy of the Italian peninsula that might be key in understanding the start of its relative decline compared to the emerging northern European countries.

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We analyze forward-induction reasoning in games with asymmetric information assuming some commonly understood restrictions on beliefs. Specifically, we assume that some given restrictions Δ on players' initial or conditional first-order beliefs are transparent, that is, not only the restrictions Δ hold, but there is common belief in Δ at every node. Most applied models of asymmetric information are covered as special cases whereby Δ pins down the probabilities initially assigned to states of nature. But the abstract analysis also allows for transparent restrictions on beliefs about behavior, e.g. independence restrictions or restrictions induced by the context behind the game. Our contribution is twofold. First, we use dynamic interactive epistemology to formalize assumptions that capture foward-induction reasoning given the transparency of Δ, and show that the behavioral implications of these assumptions are characterized by the Δ-rationalizability solution procedure of Battigalli (1999, 2003). Second, we study the differences and similarities between this solution concept and a simpler solution procedure put forward by Battigalli and Siniscalchi (2003). We show that the two procedures are equivalent if Δ is 'closed under compositions', a property that holds in all the applications considered by Battigalli and Siniscalchi (2003). We also show that when Δ is not closed under compositions the simpler solution procedure may fail to characterize the behavioral implications of forward induction reasoning.

Interactive epistemology in dynamic games studies forms of strategic reasoning like backward induction and forward induction by formally representing the players' beliefs about each other, conditional on each history. Work on this topic typically relies on epistemic models where states of the world specify both strategies and beliefs. In this literature, strategies are interpreted as objective descriptions of what the players would choose at each history. But the intuitive interpretation of strategy is that of (subjective) contingent plan of action. As players do not delegate their moves to devices that mechanically execute a strategy, plans cannot be anything but beliefs of players about their own behavior. In this paper we analyze strategic reasoning in dynamic games with perfect information by means of epistemic models where behavior is described only by the play path, and players' beliefs include their contingent plans. We define rational planning, a property of beliefs only, and material consistency, which connects plans with choices on the play path. Material rationality is the conjunction of rational planning and material consistency. In perfect information games of depth two, the simplest dynamic games, correct belief in material rationality only implies a Nash outcome, not the backward-induction one. We have to consider stronger assumptions of persistence of belief in material rationality in order to obtain backward induction and forward induction. We relate our work to the existing literature, and we discuss the extension of our analysis to games with imperfect information.

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Trafficking of persons is a serious and very complex issue, although too often neglected, in many developing countries, including the Philippines. We make a first attempt to produce empirical research from the angle of development economists to assess the risk factors for entering into trafficking and evaluate the prospects of reintegration of trafficked victims. We have interviewed young women resident in shelters in the Cebu area and the sample consists of girls 14 years and above living in 12 shelters in the Cebu area. We find that trafficked victims have on average lower levels of education than the non-trafficked girls. Trafficking victims are also more likely to come from larger families. 20 percent of the girls came from households where the mother was absent during the last year she lived with her family. Therefore, as expected, income appears as a main factor of vulnerability. Any policy oriented to create safety nets for families at risk, empowering women, and create better labor opportunities for girls is likely to reduce to probabilities of entering into trafficking. In terms of family dynamics, trafficking victims come from families with relatively more inter-personal conflicts. There is also more prevalence of physical violence in houses where trafficked victims lived. The violent home environment of these vulnerable girls needs to be kept in mind when designing reintegration programs. Using techniques that elicit the expectations that the girls had when leaving their household and then comparing them with what actually happened, we observe that trafficked girls underestimate the cost of leaving the household (in terms of likelihood to get pregnant, ill, use drugs) and overestimate the benefits (in terms of likelihood to marry a foreign man and being able to send back money to the family). Moreover, we also find that friends are the most prevalent mode of recruitment of trafficking while the role of formal recruiters is less important. In our sample, only 27 percent of the girls obtained their job via a recruiter. Information campaigns to explain the danger of the jobs offered could contribute to stopping the trafficking phenomenon. Finally, important insights emerged by looking at inter-temporal preferences and risk preferences of our respondents, where these preferences were elicited using the tools of experimental economics. Former victims of trafficking exhibited a relatively high degree of impatience compared to other girls. On the other hand, both groups were extremely risk averse. These results suggests that an important role should be given, when designing reintegration programs for vulnerable girls – and especially former victims of trafficking – in working on the formation of their expectation, inter-temporal preferences and risk preferences.

We derive the analogue of the classic Arrow-Pratt approximation of the certainty equivalent under model uncertainty as defined by the smooth model of decision making under ambiguity of Klibanoff, Marinacci and Mukerji (2005). We study its scope via a portfolio allocation exercise that delivers a tractable mean-variance model adjusted for model uncertainty. In a problem with a risk-free asset, a risky asset, and an ambiguous asset, we find that portfolio rebalancing in response to higher model uncertainty only depends on the ambiguous asset's alpha, setting the performance of the risky asset as benchmark. In addition, the portfolios recommended by our model are not systematically conservative on the share held in the ambiguous asset: indeed, in general, it is not true that greater ambiguity reduces the optimal demand for the ambiguous asset. The analytical tractability of the enhanced Arrow-Pratt approximation renders our model especially well suited for calibration exercises aimed at exploring the consequences of ambiguity aversion on equilibrium asset prices.

'Crises feed uncertainty. And uncertainty affects behaviour, which feeds the crisis.'
Olivier Blanchard, The Economist, January 29, 2009

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This paper presents a new model of occupational licensing, where producers are heterogeneous both in their ability or productivity and in the level of the barriers to entry in the profession that they face. The model bears important implications on the effects of liberalization policies that differ dramatically from those implied by the standard model, where heterogeneity is unidimensional in productivity. Specifically, we find that liberalization policies induce higher quality of services if barriers to entry are high for the most able agents. The opposite if such a correlation is low. We test these implications using detailed microdata on Italian lawyers and find a strong effect of the 2006 Italian liberalizing reform on the composition of the outflows from the legal profession. While higher ability lawyers are more likely to leave the profession before the reform, the opposite happens in its aftermaths, consistently with the idea that monopoly power selects high-productivity lawyers out of the profession.

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