Conditional Moments and Independence

Consider two random variables X and Y. In initial probability and statistics courses, a discussion of various concepts of dissociation between X and Y is customary. These concepts typically involve independence and uncorrelatedness. An example is shown where E(Y^n|X) = E(Y^n) and E(X^n|Y) = E(X^n) for n = 1, 2,… and yet X and Y are not stochastically independent. The bi-variate distribution is constructed using a well-known example in which the distribution of a random variable is not uniquely determined by its sequence of moments. Other similar families of distributions with identical moments can be used to display such a pair of random variables. It is interesting to note in class that even such a degree of dissociation between the moments of X and Y does not imply stochastic independence. and yet X and Y are not stochastically independent. The bi-variate distribution is constructed using a well-known example in which the distribution of a random variable is not uniquely determined by its sequence of moments. Other similar families of distributions with identical moments can be used to display such a pair of random variables. It is interesting to note in class that even such a degree of dissociation between the moments of X and Y does not imply stochastic independence.indeterminate distributions, moments, independence

Inference in a Synchronization Game with Social Interactions

This paper studies inference in a continuous-time game where an agent’s decision to quit an activity depends on the participation of other players. In equilibrium, similar actions can be explained not only by direct influences, but also by correlated factors. Our model can be seen as a simultaneous duration model with multiple decision makers and interdependent durations. We study the problem of determining existence and uniqueness of equilibrium stopping strategies in this setting. This paper provides results and conditions for the detection of these endogenous effects. First, we show that the presence of such effects is a necessary and sufficient condition for simultaneous exits. This allows us to set up a nonparametric test for the presence of such influences which is robust to multiple equilibria. Second, we provide conditions under which parameters in the game are identified. Finally, we apply the model to data on desertion in the Union Army during the American Civil War and find evidence of endogenous influences.duration models; social interactions; empirical games; optimal stopping

Inference in a Synchronization Game with Social Interactions, Second Version

This paper studies inference in a continuous time game where an agent's decision to quit an activity depends on the participation of other players. In equilibrium, similar actions can be explained not only by direct influences but also by correlated factors. Our model can be seen as a simultaneous duration model with multiple decision makers and interdependent durations. We study the problem of determining the existence and uniqueness of equilibrium stopping strategies in this setting. This paper provides results and conditions for the detection of these endogenous effects. First, we show that the presence of such effects is a necessary and sufficient condition for simultaneous exits. This allows us to set up a nonparametric test for the presence of such influences which is robust to multiple equilibria. Second, we provide conditions under which parameters in the game are identified. Finally, we apply the model to data on desertion in the Union Army during the American Civil War and find evidence of endogenous influences.duration models, social interactions, empirical games, optimal stopping

Identification and Estimation of Preference Distributions When Voters Are Ideological

This paper studies the nonparametric identification and estimation of voters' preferences when voters are ideological. We build on the methods introduced by Degan and Merlo (2009) representing elections as Voronoi tessellations of the ideological space. We exploit the properties of this geometric structure to establish that voter preference distributions and other parameters of interest can be identified from aggregate electoral data. We also show that these objects can be consistently estimated using the methodology proposed by Ai and Chen (2003) and we illustrate our analysis by performing an actual estimation using data from the 1999 European Parliament elections.Voting, Voronoi tessellation,identification, nonparametric

Inference of Signs of Interaction Effects in Simultaneous Games with Incomplete Information, Second Version

This paper studies the inference of interaction effects, i.e., the impacts of players' actions on each other's payoffs, in discrete simultaneous games with incomplete information. We propose an easily implementable test for the signs of state-dependent interaction effects that does not require parametric specifications of players' payoffs, the distributions of their private signals or the equilibrium selection mechanism. The test relies on the commonly invoked assumption that players' private signals are independent conditional on observed states. The procedure is valid in the presence of multiple equilibria, and, as a by-product of our approach, we propose a formal test for multiple equilibria in the data-generating process. We provide Monte Carlo evidence of the test's good performance infinite samples. We also implement the test to infer the direction of interaction effects in couples' joint retirement decisions using data from the Health and Retirement Study.identification, inference, multiple equilibria, incomplete information games

Inference of Signs of Interaction Effects in Simultaneous Games with Incomplete Information

This paper studies the inference of interaction effects, i.e., the impacts of players' actions on each other's payoffs, in discrete simultaneous games with incomplete information. We propose an easily implementable test for the signs of state-dependent interaction effects that does not require parametric specifications of players' payoffs, the distributions of their private signals or the equilibrium selection mechanism. The test relies on the commonly invoked assumption that players' private signals are independent conditional on observed states. The procedure is valid in the presence of multiple equilibria, and, as a by-product of our approach, we propose a formal test for multiple equilibria in the data-generating process. We provide Monte Carlo evidence of the test's good performance in finite samples. We also implement the test to infer the direction of interaction effects in couples' joint retirement decisions using data from the Health and Retirement Study.identification, inference, multiple equilibria, incomplete information games

Inference of Signs of Interaction Effects in Simultaneous Games with Incomplete Information, Second Version

This paper studies the inference of interaction effects (impacts of players' actions on each other's payoffs) in discrete simultaneous games with incomplete information. We propose an easily implementable test for the signs of state-dependent interaction effects that does not require parametric specifications of players' payoffs, the distributions of their private signals or the equilibrium selection mechanism. The test relies on the commonly invoked assumption that players' private signals are independent conditional on observed states. The procedure is valid in (but does not rely on) the presence of multiple equilibria in the data-generating process (DGP). As a by-product, we propose a formal test for multiple equilibria in the DGP. We also show how to extend our arguments to identify signs of interaction effects when private signals are correlated. We provide Monte Carlo evidence of the test's good performance in finite samples. We then implement the test using data on radio programming of commercial breaks in the U.S., and infer stations' incentives to synchronize their commercial breaks. Our results support the earlier finding by Sweeting (2009) that stations have stronger incentives.identification, inference, multiple equilibria, incomplete information games

Interdependent Durations

This paper studies the identification of a simultaneous equation model where the variable of interest is a duration measure. It proposes a game theoretic model in which durations are determined by strategic agents. In the absence of strategic motives, the model delivers a version of the generalized accelerated failure time model. In its most general form, the system resembles a classical simultaneous equation model in which endogenous variables interact with observable and unobservable exogenous components to characterize a certain economic environment. In this paper, the endogenous variables are the individually chosen equilibrium durations. Even though a unique solution to the game is not always attainable in this context, the structural elements of the economic system are shown to be semiparametrically point identified. We also present a brief discussion of estimation ideas and a set of simulation studies on the model.duration, empirical games, identification

The Informal Sector, Third Version

This paper investigates the determinants of informal economic activity. We present two equilibrium models of informality and test their implications using a survey of 48,000+ small firms in Brazil. We define informality as tax avoidance; firms in the informal sector avoid tax payments but suffer other limitations. In the first model there is a single industry and informal firms face a higher cost of capital and a limitation on size. As a result informal firms are smaller and have a lower capital-labor ratio. When education is an imperfect proxy for ability, we show that the interaction of the manager's education and formality has a positive correlation with firm size. These implications are supported by our empirical analysis. A novel theoretical contribution in this paper is a model that highlights the role of value added taxes in transmitting informality. It predicts that the informality of a firm is correlated to the informality of firms from which it buys or sells. The model also implies that higher tolerance for informal firms in one production stage increases tax avoidance in downstream and upstream sectors. Empirical analysis shows that, in fact, various measures of formality of suppliers and purchasers (and its enforcement) are correlated with the formality of a firm. Even more interestingly, when we look at sectors where Brazilian firms are not subject to the credit system of value added tax, but instead the value added tax is applied at some stage of production at a rate that is estimated by the State, this chain effect vanishes.Informal Sector, VAT, Tax Avoidance