Essays on Uncertainty, Imperfect Information, and Investment Dynamics

Understanding how imperfect information affects firms' investment decision helps answer important questions in economics, such as how we may better measure economic uncertainty; how firms' forecasts would affect their decision-making when their beliefs are not backed by economic fundamentals; and how important are the business cycle impacts of changes in firms' productivity uncertainty in an environment of incomplete information. This dissertation provides a synthetic answer to all these questions, both empirically and theoretically. The first chapter, provides empirical evidence to demonstrate that survey-based forecast dispersion identifies a distinctive type of second moment shocks different from the canonical volatility shocks to productivity, i.e. uncertainty shocks. Such forecast disagreement disturbances can affect the distribution of firm-level beliefs regardless of whether or not belief changes are backed by changes in economic fundamentals. At the aggregate level, innovations that increase the dispersion of firms' forecasts lead to persistent declines in aggregate investment and output, which are followed by a slow recovery. On the contrary, the larger dispersion of future firm-specific productivity innovations, the standard way to measure economic uncertainty, delivers the ``wait and see" effect, such that aggregate investment experiences a sharp decline, followed by a quick rebound, and then overshoots. At the firm level, data uncovers that more productive firms increase investments given rises in productivity dispersion for the future, whereas investments drop when firms disagree more about the well-being of their future business conditions. These findings challenge the view that the dispersion of the firms' heterogeneous beliefs captures the concept of economic uncertainty, defined by a model of uncertainty shocks. The second chapter presents a general equilibrium model of heterogeneous firms subject to the real productivity uncertainty shocks and informational disagreement shocks. As firms cannot perfectly disentangle aggregate from idiosyncratic productivity because of imperfect information, information quality thus drives the wedge of difference between the unobserved productivity fundamentals, and the firms' beliefs about how productive they are. Distribution of the firms' beliefs is no longer perfectly aligned with the distribution of firm-level productivity across firms. This model not only explains why, at the macro and micro level, disagreement shocks are different from uncertainty shocks, as documented in Chapter 1, but helps reconcile a key challenge faced by the standard framework to study economic uncertainty: a trade-off between sizable business cycle effects due to changes in uncertainty, and the right amount of pro-cyclicality of firm-level investment rate dispersion, as measured by its correlation with the output cycles.

A Visual Analytics Approach to Comparing Cohorts of Event Sequences

Sequences of timestamped events are currently being generated across nearly every domain of data analytics, from e-commerce web logging to electronic health records used by doctors and medical researchers. Every day, this data type is reviewed by humans who apply statistical tests, hoping to learn everything they can about how these processes work, why they break, and how they can be improved upon. To further uncover how these processes work the way they do, researchers often compare two groups, or cohorts, of event sequences to find the differences and similarities between outcomes and processes. With temporal event sequence data, this task is complex because of the variety of ways single events and sequences of events can differ between the two cohorts of records: the structure of the event sequences (e.g., event order, co-occurring events, or frequencies of events), the attributes about the events and records (e.g., gender of a patient), or metrics about the timestamps themselves (e.g., duration of an event). Running statistical tests to cover all these cases and determining which results are significant becomes cumbersome. Current visual analytics tools for comparing groups of event sequences emphasize a purely statistical or purely visual approach for comparison. Visual analytics tools leverage humans' ability to easily see patterns and anomalies that they were not expecting, but is limited by uncertainty in findings. Statistical tools emphasize finding significant differences in the data, but often requires researchers have a concrete question and doesn't facilitate more general exploration of the data. Combining visual analytics tools with statistical methods leverages the benefits of both approaches for quicker and easier insight discovery. Integrating statistics into a visualization tool presents many challenges on the frontend (e.g., displaying the results of many different metrics concisely) and in the backend (e.g., scalability challenges with running various metrics on multi-dimensional data at once). I begin by exploring the problem of comparing cohorts of event sequences and understanding the questions that analysts commonly ask in this task. From there, I demonstrate that combining automated statistics with an interactive user interface amplifies the benefits of both types of tools, thereby enabling analysts to conduct quicker and easier data exploration, hypothesis generation, and insight discovery. The direct contributions of this dissertation are: (1) a taxonomy of metrics for comparing cohorts of temporal event sequences, (2) a statistical framework for exploratory data analysis with a method I refer to as high-volume hypothesis testing (HVHT), (3) a family of visualizations and guidelines for interaction techniques that are useful for understanding and parsing the results, and (4) a user study, five long-term case studies, and five short-term case studies which demonstrate the utility and impact of these methods in various domains: four in the medical domain, one in web log analysis, two in education, and one each in social networks, sports analytics, and security. My dissertation contributes an understanding of how cohorts of temporal event sequences are commonly compared and the difficulties associated with applying and parsing the results of these metrics. It also contributes a set of visualizations, algorithms, and design guidelines for balancing automated statistics with user-driven analysis to guide users to significant, distinguishing features between cohorts. This work opens avenues for future research in comparing two or more groups of temporal event sequences, opening traditional machine learning and data mining techniques to user interaction, and extending the principles found in this dissertation to data types beyond temporal event sequences.

Parsing, Generation and Grammar

Humans use their grammatical knowledge in more than one way. On one hand, they use it to understand what others say. On the other hand, they use it to say what they want to convey to others (or to themselves). In either case, they need to assemble the structure of sentences in a systematic fashion, in accordance with the grammar of their language. Despite the fact that the structures that comprehenders and speakers assemble are systematic in an identical fashion (i.e., obey the same grammatical constraints), the two ‘modes’ of assembling sentence structures might or might not be performed by the same cognitive mechanisms. Currently, the field of psycholinguistics implicitly adopts the position that they are supported by different cognitive mechanisms, as evident from the fact that most psycholinguistic models seek to explain either comprehension or production phenomena. The potential existence of two independent cognitive systems underlying linguistic performance doubles the problem of linking the theory of linguistic knowledge and the theory of linguistic performance, making the integration of linguistics and psycholinguistic harder. This thesis thus aims to unify the structure building system in comprehension, i.e., parser, and the structure building system in production, i.e., generator, into one, so that the linking theory between knowledge and performance can also be unified into one. I will discuss and unify both existing and new data pertaining to how structures are assembled in understanding and speaking, and attempt to show that the unification between parsing and generation is at least a plausible research enterprise. In Chapter 1, I will discuss the previous and current views on how parsing and generation are related to each other. I will outline the challenges for the current view that the parser and the generator are the same cognitive mechanism. This single system view is discussed and evaluated in the rest of the chapters. In Chapter 2, I will present new experimental evidence suggesting that the grain size of the pre-compiled structural units (henceforth simply structural units) is rather small, contrary to some models of sentence production. In particular, I will show that the internal structure of the verb phrase in a ditransitive sentence (e.g., The chef is donating the book to the monk) is not specified at the onset of speech, but is specified before the first internal argument (the book) needs to be uttered. I will also show that this timing of structural processes with respect to the verb phrase structure is earlier than the lexical processes of verb internal arguments. These two results in concert show that the size of structure building units in sentence production is rather small, contrary to some models of sentence production, yet structural processes still precede lexical processes. I argue that this view of generation resembles the widely accepted model of parsing that utilizes both top-down and bottom-up structure building procedures. In Chapter 3, I will present new experimental evidence suggesting that the structural representation strongly constrains the subsequent lexical processes. In particular, I will show that conceptually similar lexical items interfere with each other only when they share the same syntactic category in sentence production. The mechanism that I call syntactic gating, will be proposed, and this mechanism characterizes how the structural and lexical processes interact in generation. I will present two Event Related Potential (ERP) experiments that show that the lexical retrieval in (predictive) comprehension is also constrained by syntactic categories. I will argue that the syntactic gating mechanism is operative both in parsing and generation, and that the interaction between structural and lexical processes in both parsing and generation can be characterized in the same fashion. In Chapter 4, I will present a series of experiments examining the timing at which verbs’ lexical representations are planned in sentence production. It will be shown that verbs are planned before the articulation of their internal arguments, regardless of the target language (Japanese or English) and regardless of the sentence type (active object-initial sentence in Japanese, passive sentences in English, and unaccusative sentences in English). I will discuss how this result sheds light on the notion of incrementality in generation. In Chapter 5, I will synthesize the experimental findings presented in this thesis and in previous research to address the challenges to the single system view I outlined in Chapter 1. I will then conclude by presenting a preliminary single system model that can potentially capture both the key sentence comprehension and sentence production data without assuming distinct mechanisms for each.

Multi-level, Multi-stage and Stochastic Optimization Models for Energy Conservation in Buildings for Federal, State and Local Agencies

Energy Conservation Measure (ECM) project selection is made difficult given real-world constraints, limited resources to implement savings retrofits, various suppliers in the market and project financing alternatives. Many of these energy efficient retrofit projects should be viewed as a series of investments with annual returns for these traditionally risk-averse agencies. Given a list of ECMs available, federal, state and local agencies must determine how to implement projects at lowest costs. The most common methods of implementation planning are suboptimal relative to cost. Federal, state and local agencies can obtain greater returns on their energy conservation investment over traditional methods, regardless of the implementing organization. This dissertation outlines several approaches to improve the traditional energy conservations models. Any public buildings in regions with similar energy conservation goals in the United States or internationally can also benefit greatly from this research. Additionally, many private owners of buildings are under mandates to conserve energy e.g., Local Law 85 of the New York City Energy Conservation Code requires any building, public or private, to meet the most current energy code for any alteration or renovation. Thus, both public and private stakeholders can benefit from this research. The research in this dissertation advances and presents models that decision-makers can use to optimize the selection of ECM projects with respect to the total cost of implementation. A practical application of a two-level mathematical program with equilibrium constraints (MPEC) improves the current best practice for agencies concerned with making the most cost-effective selection leveraging energy services companies or utilities. The two-level model maximizes savings to the agency and profit to the energy services companies (Chapter 2). An additional model presented leverages a single congressional appropriation to implement ECM projects (Chapter 3). Returns from implemented ECM projects are used to fund additional ECM projects. In these cases, fluctuations in energy costs and uncertainty in the estimated savings severely influence ECM project selection and the amount of the appropriation requested. A risk aversion method proposed imposes a minimum on the number of “of projects completed in each stage. A comparative method using Conditional Value at Risk is analyzed. Time consistency was addressed in this chapter. This work demonstrates how a risk-based, stochastic, multi-stage model with binary decision variables at each stage provides a much more accurate estimate for planning than the agency’s traditional approach and deterministic models. Finally, in Chapter 4, a rolling-horizon model allows for subadditivity and superadditivity of the energy savings to simulate interactive effects between ECM projects. The approach makes use of inequalities (McCormick, 1976) to re-express constraints that involve the product of binary variables with an exact linearization (related to the convex hull of those constraints). This model additionally shows the benefits of learning between stages while remaining consistent with the single congressional appropriations framework.