Latent Variable and Long-Memory Models

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The proposed work is divided into two projects. The first project develops computationally efficient statistical inference techniques for classes of set identified models. Such models are helpful because they seek, under minimal assumptions, to usefully constrain the possible values of a model's parameters while avoiding the unnecessarily strong assumptions that would be needed to isolate a unique solution. Specifically, this project considers set identified models that arise from the presence of unobservable variables in the model and that have characteristics that traditionally demand a high-dimensional treatment. The methods proposed aim to express asymptotic properties in terms of a combination of simpler low-dimensional building blocks and may thus offer considerable advantages over existing generic brute-force simulation methods. The second project explores a connection between two apparently disparate concepts: (i) long memory (i.e. shocks have persistent effects on a dynamical system) and (ii) network structure. This project demonstrates that long memory can naturally arise when a large number of subsystems with a short memory are interconnected to form a network such that the outputs of each of the subsystems are fed into the inputs of others. This results in a collective behavior that is richer than that of individual subsystems. The long-memory behavior is found to be primarily determined by the geometry of the network rather than by the specific dynamic response of individual subsystems. These finding are interesting because, although long-memory processes are routinely used in time series modeling, a simple constructive explanation for their occurrence had so far remained difficult to find.Set identified models are becoming widely used in statistics and economics, and this trend will likely continue, especially if inference methods can be made simpler and computationally more efficient. Fields as diverse as medicine and climate change could also benefit from formal methods acknowledging that some parameters cannot be precisely known but can plausibly be bounded. Understanding how network structure influences the dynamics of an economy is a central question, especially in the context of the recent credit crisis. The collective behavior of networks has clear applications in social sciences in general, including psychology, the study of social media, and even computer networks, which are being increasingly relied upon for infrastructure management and logistics.