COLLABORATIVE RESEARCH INCOMPLETE INFORMATION IN DYNAMIC ECONOMIES:ANALYTICS AND APPLICATIONS
Since the rational expectations revolution, solving for equilibria in dynamic macroeconomic models relies on imposing the restriction that model dynamics are a function of expectations of stochastic variables. Following the intuition of Pigou (1929) - that structural features of the economy coupled with incomplete information may lead to waves of pessimism and optimism -incomplete information played a prominent role in the early macroeconomic rational expectations literature [see Lucas (1972) and Kydland and Prescott (1982)]. Despite the potential for generating an interesting set of results, informational frictions soon disappeared from the literature, primarily due to the technical challenges that emerge when solving for dynamic models with incomplete information. The PI's research will return to paradigm of the early literature and examine how incomplete information affects equilibrium outcomes. 1. Intellectual Merit The intellectual merit of the proposed research is to fully specify and characterize "information equilibria" in dynamic economies. The proposed research will (1) Establish an information equilibrium concept that provides existence and uniqueness conditions for dynamic models with incomplete information. Preliminary results suggest that the PIs' equilibrium concept overturns non-existence results once thought to be pervasive in models with non-trivial informational dynamics. (2) Analytically characterize the space of information equilibria for dynamic rational expectations models. The proposed approach overcomes the technical challenges of solving for equilibrium and achieves a closed-form characterization of the equilibria by solving the model in the space of analytic functions. (3) Characterize the dynamic properties of the class of information equilibria for which endowed asymmetric information survives in equilibrium. The PIs characterize higher-order belief dynamics in closed form and demonstrate an important propagation effect due to incomplete information. (4) Provide a novel informational interpretation of moving average representations by deriving an equivalence between non-fundamental moving average representations and dynamic signal extraction problems. (5) Examine how incomplete information alters equilibrium dynamics in a variety of settings. Preliminary results suggest that incomplete information can play a vital role in assessing the sources of business cycle dynamics, determining optimal information disclosure and stabilization policies, reconciling asset pricing theory with data, and improving the empirical fit of macro DSGE models; to name a few applications. 2. Broader Impact By focusing on dynamic uncertainty in very general setups, the PI's believe the contributions can have a broad impact in many areas of dynamic economics. While the PIs research focuses on macro and finance, incomplete information and the solution techniques can be applied more broadly. The proposed research will make a concerted effort to make clear the advantages of the employed techniques by providing an explicit connection between the concepts of the proposed research and existing methodologies that are more familiar to the profession.
The Great Recession and worldwide financial crisis of 2007--2012 is the deepest and most severe recession since the Great Depression. The Federal Reserve and other policy-making institutions have responded to the crisis with unprecedented action. Understanding the cause and consequences of the recession, and how the policy response will affect the economy is a difficult task. Recent economic events motivate much of my research supported by Federal Award 0962221. My research falls into two categories---expectations formation and policy analysis, a natural demarcation both in content and in intended audience. Work on expectations formation is more theoretical and academic, while research on monetary and fiscal policy is more applied and garners interest both inside and outside the academy (for example from central bankers and policy makers). Heterogeneous Beliefs: The idea that different agents in an economy may hold different beliefs is intuitive. It is also underdeveloped because formal models of heterogeneous beliefs pose formidable technical challenges. The motivation behind heterogeneous beliefs dates back to the British economist John Maynard Keynes who hypothesized that heterogenous beliefs explain the fickle behavior of financial markets. He believed that traders not only had to guess what tomorrow's stock price would be, but also what other traders thought tomorrow's stock price would be. Keynes referred to these beliefs as ``higher-order beliefs.'' Keeping track of higher-order beliefs in a formal model with several traders who are buying and selling several assets is technically demanding. Rondina and Walker (2012, 2013a, 2013b) and Kasa, Walker, and Whiteman (2012) develop methods to solve dynamic models of macroeconomics and finance with heterogeneous beliefs. In my joint work with Giacomo Rondina, we derive analytic representations for the higher-order beliefs, whereas earlier work relied on numerical approximations. Analytic solutions are an important contribution that opens the door to address a host of fresh questions that previous methods could not answer. For example, we show that contrary to recent findings, higher-order beliefs can generate positive effects on information diffusion: if dispersedly informed agents were not engaging in formulating expectations about expectations about expectations and so on, information transmission through equilibrium prices would be reduced. That is, higher-order beliefs enhance the information content of prices. Asset Pricing: Asset-pricing anomalies are a chief challenge for rational expectations theories. A rational expectations, representative agent view of asset pricing implies that asset prices follow a random walk and are related in a particular way to the underlying dividend process of the asset. Beginning in the 1980s, it became clear that this simple view of the world cannot explain asset-pricing data. Two prominent examples of asset-pricing anomalies are that asset prices are too volatile relative to fundamentals (excess volatility puzzle) and investors seem to prefer bonds over stocks at rates that far exceed ``rational behavior" (equity premium puzzle). Kasa, Walker and Whiteman (2012) returns to Keynes's question to ask whether higher-order beliefs help explain asset pricing anomalies. We demonstrate that higher-order belief dynamics can partially explain excess volatility. The intuition is that because investors care not only about the value of the underlying fundamentals (dividends), but also about the predictions of other traders, asset prices can drift away from fundamental values. If the drift is significant enough, asset price dynamics from our model can replicate what we see in data. Foresight: Although rational expectations was only recently formalized, the idea that economic fluctuations arise in part from economic decision makers' responses to expectations about not-yet-realized economic fundamentals dates at least to Pigou (1927). The Great Recession has generated a renewed interest in Pigou's theories. His insights find voice in a recent surge of research examining the economic consequences of news or foresight. My work in this area aims to systematically examine how information flows affect the nature of equilibrium and the connection of theory to data. Leeper, Walker and Yang (2012) and Leeper, Walker and Richter (2010) focus on how to identify and quantify the impacts of foreseen ``shocks" to taxes. Taxes are a natural choice because few economic phenomena provide economic agents with such clear signals about how important margins will change in the future: foresight is intrinsic to the political process that determines taxes. Leeper and Walker (2009) show how information flows can generate recessions along the lines of Pigou (1927). Over the course of the grant, I have published 10 papers and have 5 papers under review for publication. All of these papers were supported by Federal Award 0962221. I have given over 25 presentations at academic institutions, monetary and fiscal policy agencies and well-respected conferences. Solution techniques, with publicly available computational code, was developed. I also developed extensive teaching material and a graduate-level course based on the findings of the grant.
