Ambiguity, Business Cycle Dynamics and Optimal Policy

Duke University, Durham NC

Investigators

Abstract

Abstract Proposal Title: Ambiguity, Business Cycle Dynamics and Optimal Policy Proposal Number: SES ? 1261014 Principal Investigator: llut, Cosmin This proposal starts from two observations. On the one hand, a large body of evidence suggests that humans perceive ambiguous situations (that is, uncertain situations where probabilities are not known) differently from risky situations (where probabilities are known). Arguably the majority of decisions made on a daily basis by investors and businesses are made under ambiguity. On the other hand, there is a large literature in economics that attempts to understand the quantitative implications of decision makers' attitudes towards uncertainty for asset prices and the business cycle. This literature has almost exclusively assumed that decision makers behave as if probabilities are known. It has so far met with limited success: a number of "puzzles" show that standard models cannot reconcile the volatility of business cycle quantities with the level and volatility of asset prices and investors' asset positions. This casts doubt on how useful these models are for evaluating policy in uncertain situations. This proposal describes a new approach to building macroeconomic models with ambiguity-averse decision makers. In terms of methodology, the proposal provides a simple way to build, solve and estimate such models. In particular, the approach accommodates time variation in the ambiguity perceived by agents about different sources of uncertainty, such as productivity or policy parameters. The approach also suggests how to connect uncertainty measured by an econometrician to the uncertainty perceived by economic agents in a model. The proposed research analyzes how to use the new tools to show that ambiguity is a promising model ingredient for understanding business cycle dynamics, asset price volatility and optimal policy. To model agents? attitude towards ambiguity, the proposed approach builds on developed decision-theoretical foundations. In particular the approach uses the multiple priors utility model, according to which agents act as if they evaluate plans using a worst case probability drawn from a set of multiple beliefs. If agents have less confidence in probability assessments on the uncertain events then the set of beliefs is larger. In a dynamic model, one reason for a change in the size of the belief set is the arrival of information. For example, a loss of confidence could be triggered by worrisome information about the future. Conversely, an increase in confidence -- captured by shrinkage of the set of beliefs -- could occur as agents might learn reassuring information that moves them closer toward thinking in terms of probabilities. In either case, agents respond to a change in confidence if the worst case probability used to evaluate actions also changes. In a macroeconomic model, uncertainty comes from a variety of sources, summarized by a number of exogenous shocks. Examples include contemporaneous changes to technology or the policy regime, but also news about those issues in the future. The proposed approach to constructing belief sets for agents with multiple priors utility is the following. At every date, the set of beliefs about a shock next period is parameterized by an interval of means centered around zero. A loss of confidence is then captured by an increase in the width of the interval; in particular, the "worst case" mean becomes worse. Conversely, an increase in confidence is captured by a narrowing of the interval and thereby a better worst case mean. Since agents take actions based on the worst case mean, a change in confidence works like news shock: an agent who gains (losses) confidence responds as if he had received good (bad) news about the future. The analysis of confidence shocks is particularly tractable in economies that are essentially linear, that is, the worst case means supporting agents' equilibrium choices can be written as a linear function of the state variables. This property implies that equilibria can be accurately characterized using first order approximations. In particular, the proposed research can study agents' responses to changes in uncertainty, as well as time variation in uncertainty premia on assets, without resorting to higher order approximations. This is in sharp contrast to the case of changes in risk, where higher order solutions are critical. An important goal of the proposed research is to quantify the effects of confidence shocks in driving the US business cycle and asset prices. In particular, one application is to incorporate agents? ambiguity about productivity into a standard quantitative DSGE model and allow their confidence to vary over time, a type of "uncertainty shock". Even though uncertainty shocks are present, standard linearization methods can be used to solve and estimate the model. Preliminary results suggest that such time-varying ambiguity can emerge as a major source of business cycle fluctuations. The proposed research also aims to make progress in understanding movements in asset prices. Here the important insight is that time variation in ambiguity leads econometricians to measure time varying premia in asset markets. Indeed, when investors evaluate an asset as if the mean payoff is low, then they are willing to pay only a low price for it. To an econometrician, the return on the asset -- actual payoff minus price -- will then look unusually high. The more ambiguity investors perceive, the lower is the price and the higher is the subsequent return. The proposal aims to address issues such as the magnitude of average asset premia, which are puzzlingly low in rational expectations models, and time-variation in excess returns in a quantitative model that can be fit to the data. This research will have a broad impact, in part, because it brings diverse areas of economic research into greater contact with one another. Specifically, the proposal links advances in decision theory to areas in macroeconomics and finance such as business cycles, asset pricing, and optimal policy. So the project should enhance synergies across sub-disciplines. The proposal should also lead to progress in understanding environments in which agents? confidence matters for the economy, which is important for positive and normative analysis. The project has the potential of having a significant impact on how policy makers analyze such complex environments, including stabilization policies, the functioning of financial markets, booms and crashes in asset prices and real activity.