Estimating equilibrium models of sorting across locations

While there is growing interest in measuring the size and scope of local spillovers, it is well understood that such spillovers cannot be distinguished from unobservable local attributes using solely the observed location decisions of individuals or firms. We propose an empirical strategy for recovering estimates of spillovers in the presence of unobserved local attributes for a broadly applicable class of equilibrium sorting models. Our approach relies on an IV strategy derived from the internal logic of the sorting model itself. We show practically how the strategy is implemented, provide intuition for our instruments, discuss the role of effective choice-set variation in identifying the model, and carry-out a series of Monte Carlo simulations to demonstrate performance in small samples. © 2007 The Author(s). Journal compilation Royal Economic Society 2007.

Invariant measure selection by noise. An example

We consider a deterministic system with two conserved quantities and infinity many invariant measures. However the systems possess a unique invariant measure when enough stochastic forcing and balancing dissipation are added. We then show that as the forcing and dissipation are removed a unique limit of the deterministic system is selected. The exact structure of the limiting measure depends on the specifics of the stochastic forcing.

The centrality of event scale: a measure of integrating a trauma into one's identity and its relation to post-traumatic stress disorder symptoms.

We introduce a new scale that measures how central an event is to a person's identity and life story. For the most stressful or traumatic event in a person's life, the full 20-item Centrality of Event Scale (CES) and the short 7-item scale are reliable (alpha's of .94 and .88, respectively) in a sample of 707 undergraduates. The scale correlates .38 with PTSD symptom severity and .23 with depression. The present findings are discussed in relation to previous work on individual differences related to PTSD symptoms. Possible connections between the CES and measures of maladaptive attributions and rumination are considered along with suggestions for future research.

Memorability as a measure of processing: a unit analysis of prose and list learning.

The percentage of subjects recalling each unit in a list or prose passage is considered as a dependent measure. When the same units are recalled in different tasks, processing is assumed to be the same; when different units are recalled, processing is assumed to be different. Two collections of memory tasks are presented, one for lists and one for prose. The relations found in these two collections are supported by an extensive reanalysis of the existing prose memory literature. The same set of words were learned by 13 different groups of subjects under 13 different conditions. Included were intentional free-recall tasks, incidental free recall following lexical decision, and incidental free recall following ratings of orthographic distinctiveness and emotionality. Although the nine free-recall tasks varied widely with regard to the amount of recall, the relative probability of recall for the words was very similar among the tasks. Imagery encoding and recognition produced relative probabilities of recall that were different from each other and from the free-recall tasks. Similar results were obtained with a prose passage. A story was learned by 13 different groups of subjects under 13 different conditions. Eight free-recall tasks, which varied with respect to incidental or intentional learning, retention interval, and the age of the subjects, produced similar relative probabilities of recall, whereas recognition and prompted recall produced relative probabilities of recall that were different from each other and from the free-recall tasks. A review of the prose literature was undertaken to test the generality of these results. Analysis of variance is the most common statistical procedure in this literature. If the relative probability of recall of units varied across conditions, a units by condition interaction would be expected. For the 12 studies that manipulated retention interval, an average of 21% of the variance was accounted for by the main effect of retention interval, 17% by the main effect of units, and only 2% by the retention interval by units interaction. Similarly, for the 12 studies that varied the age of the subjects, 6% of the variance was accounted for by the main effect of age, 32% by the main effect of units, and only 1% by the interaction of age by units.(ABSTRACT TRUNCATED AT 400 WORDS)

Design of Scheduling Algorithms Using Game Theoretic Ideas

Scheduling a set of jobs over a collection of machines to optimize a certain quality-of-service measure is one of the most important research topics in both computer science theory and practice. In this thesis, we design algorithms that optimize {\em flow-time} (or delay) of jobs for scheduling problems that arise in a wide range of applications. We consider the classical model of unrelated machine scheduling and resolve several long standing open problems; we introduce new models that capture the novel algorithmic challenges in scheduling jobs in data centers or large clusters; we study the effect of selfish behavior in distributed and decentralized environments; we design algorithms that strive to balance the energy consumption and performance.

The technically interesting aspect of our work is the surprising connections we establish between approximation and online algorithms, economics, game theory, and queuing theory. It is the interplay of ideas from these different areas that lies at the heart of most of the algorithms presented in this thesis.

The main contributions of the thesis can be placed in one of the following categories.

1. Classical Unrelated Machine Scheduling: We give the first polygorithmic approximation algorithms for minimizing the average flow-time and minimizing the maximum flow-time in the offline setting. In the online and non-clairvoyant setting, we design the first non-clairvoyant algorithm for minimizing the weighted flow-time in the resource augmentation model. Our work introduces iterated rounding technique for the offline flow-time optimization, and gives the first framework to analyze non-clairvoyant algorithms for unrelated machines.

2. Polytope Scheduling Problem: To capture the multidimensional nature of the scheduling problems that arise in practice, we introduce Polytope Scheduling Problem (\psp). The \psp problem generalizes almost all classical scheduling models, and also captures hitherto unstudied scheduling problems such as routing multi-commodity flows, routing multicast (video-on-demand) trees, and multi-dimensional resource allocation. We design several competitive algorithms for the \psp problem and its variants for the objectives of minimizing the flow-time and completion time. Our work establishes many interesting connections between scheduling and market equilibrium concepts, fairness and non-clairvoyant scheduling, and queuing theoretic notion of stability and resource augmentation analysis.

3. Energy Efficient Scheduling: We give the first non-clairvoyant algorithm for minimizing the total flow-time + energy in the online and resource augmentation model for the most general setting of unrelated machines.

4. Selfish Scheduling: We study the effect of selfish behavior in scheduling and routing problems. We define a fairness index for scheduling policies called {\em bounded stretch}, and show that for the objective of minimizing the average (weighted) completion time, policies with small stretch lead to equilibrium outcomes with small price of anarchy. Our work gives the first linear/ convex programming duality based framework to bound the price of anarchy for general equilibrium concepts such as coarse correlated equilibrium.