Working papers results

The risk-neutral pricing formula provides the valuation of random payoffs in continuous-time markets. Despite the variety of payoffs, no arbitrage price dynamics are driven by the same (possibly stochastic) interest rate. We formalize this intuition by showing that no arbitrage prices constitute the solution of a differential equation, where interest rates are prominent. To achieve this goal, we introduce the notion of weak time-derivative, which permits to differentiate adapted processes. This instrument isolates drifts of semimartingales and it is null for martingales. Finally, we reformulate the eigenvalue problem of Hansen and Scheinkman (2009) by employing weak time-derivatives.

We experimentally test the impact of expanding access to basic bank accounts in Uganda, Malawi, and Chile. Over two years, 17%, 10%, and 3% of treatment individuals made five or more deposits, respectively. Average monthly deposits for them were at the 79th, 91st, and 96th percentiles of baseline savings. Survey data show no clearly discernible intention-to-treat effects on savings or any downstream outcomes. This suggests that policies merely focused on expanding access to basic accounts are unlikely to improve welfare noticeably since impacts, even if present, are likely small and diverse.

Consider a network of firms where a firm T is given the opportunity to innovate a product (first-generation innovation). If successful, this firm can temporarily sell this innovation to her direct neighbors because this will give her access to a larger market. However, if her direct neighbors innovate themselves on top of firm T's innovation (second-generation innovations), then firm T loses the right to sell her initial innovation to the remaining firms in the market. We analyze this game where each firm (T and her direct neighbors) has to decide at which price they want to sell their innovation. We show that the optimal price policy of each firm depends on the level of property rights protection, the position of firm T in the network, her degree and the size of the market. We then analyze the welfare implications of our model where the planner that maximizes total welfare has to decide which firm to target. We show that it depends on the level of property rights protection and on the network structure in a non-trivial way.

We study from a preferential viewpoint absolute and relative attitudes toward ambiguity determined by wealth effects. We provide different characterizations of these attitudes for a large class of preferences: monotone and continuous preferences which satisfy risk independence. We specify our results for different subclasses of preferences.

Pre-Hilbert A-Modules are a natural generalization of inner product spaces in which the scalars are allowed to be from an arbitrary algebra. In this perspective, submodules are the generalization of vector subspaces. The notion of orthogonality generalizes in an obvious way too. In this paper, we provide necessary and sufficient topological conditions for a submodule to be orthogonally complemented. We present three applications of our results. In the most important one, we obtain the Kunita-Watanabe decomposition for conditionally square-integrable martingales as an orthogonal decomposition result carried out in an opportune pre-Hilbert A-module. Second, we show that a version of Stricker's Lemma can be also derived as a corollary of our results. Finally, we provide a version of the Koopman-von Neumann decomposition theorem for a specific pre-Hilbert module which is useful in Ergodic Theory.

The results of an experiment extending Ellsberg's setup demonstrate that attitudes towards ambiguity and compound uncertainty are closely related. However, this association is much stronger when the second layer of uncertainty is subjective than when it is objective. Provided that the compound probabilities are simple enough, we find that most subjects, consisting of both students and policy makers, (1) reduce compound objective probabilities, (2) do not reduce compound subjective probabilities, and (3) are ambiguity non-neutral. By decomposing ambiguity into risk and model uncertainty, and jointly eliciting the attitudes individuals manifest towards these two types of uncertainty, we characterize individuals' degree of ambiguity aversion. Our data provides evidence of decreasing absolute ambiguity aversion and constant relative ambiguity aversion.

This paper investigates the differential response of male and female voters to competitive persuasion in political campaigns. We implemented a survey experiment during the (mixed gender) electoral race for mayor in Milan (2011), and a field experiment during the (same gender) electoral race for mayor in Cava de' Tirreni (2015). In both cases, a sample of eligible voters was randomly divided into three groups. Two were exposed to either a positive or a negative campaign by one of the opponents. The third-control-group received no electoral information. In Milan, the campaigns were administered online and consisted of a bundle of advertising tools (videos, texts, slogans). In Cava de' Tirreni, we implemented a large scale door-to-door campaign in collaboration with one of the candidates, randomizing positive vs. negative messages. In both experiments, stark gender differences emerge. Females vote more for the opponent and less for the incumbent when they are exposed to the opponent's positive campaign. Exactly the opposite occurs for males. These gender differences cannot be accounted for by gender identification with the candidate, ideology, or other observable attributes of the voters.

In this article, we provide novel survey evidence on mid schoolers' awareness and ambiguity perceptions and on how such perceptions evolve during the process of high school track choice. Children in our study display partial awareness about the set of available tracks. Additionally, children report substantial belief ambiguity about their likelihood of a regular high school path, especially for lower-ranked tracks. Students start 8th grade with greater information about their favorite alternatives and continue to concentrate their search on the latter during the months before pre-enrollment. Children from less advantaged families display lower initial perceived knowledge and acquire information at a slower pace, particularly about college-preparatory schools.

This paper provides a general framework for analyzing self-confirming policies. We study self-confirming equilibria in recurrent decision problems with incomplete information about the true stochastic model. We characterize stationary monetary policies in a linear-quadratic setting.

We study the design of child care subsidies in an optimal welfare and tax problem. The optimal subsidy schedule is qualitatively similar to the existing US scheme. Efficiency mandates a subsidy on formal child care costs for working mothers, with higher subsidies paid to lower income earners. The optimal subsidy is also kinked as a function of child care expenditure.To counterbalance the sliding scale pattern of the optimal subsidy rates, marginal labor income tax rates are set lower than the labor wedges, with the potential to generate negative marginal tax rates. We calibrate our model to features of the US labor market and focus on single mothers with children aged below 6. The optimal program provides stronger participation incentives compared to the US scheme. The intensive margin incentives provided by the efficient program are milder, with subsidy rates decreasing with income more steeply than those in the US.