Investment decisions in physical or human capital compel economic agents to look forward and predict the future. They also require an assessment of uncertain growth prospects in a complex environment. When economic agents use probability models, they face questions that are familiar from statistical decision theory and control theory. Is there a chosen benchmark model or models? Do these models depend on unknown parameters or hidden states? Could the models be misspecified? How might data be used to inform decisions? Are inferences about these hidden states important sources of uncertainty in the long run? This proposal investigates three topics that explore implications of dynamic models in which growth uncertainty is a central ingredient. This research could have broader impacts on all subfields of economics and especially the study of financial markets, business cycles and economic growth.
First, the research builds models of decentralized economies in which decision makers, private agents and policy makers, confront hidden state Markov chains in a robust manner. These models allow the investigator to explore the forward-looking aspects of capital accumulation, broadly conceived, and its associated valuation. Hidden state Markov models are valuable tools for a variety of scientific disciplines, including economics. A hidden state of a Markov chain can evolve slowly or change infrequently. When decision makers do not directly observe this state, they are compelled to use historical data on signals to make inferences about this state and when it changes. These hidden states can be sources of uncertainty with prolonged consequences. This proposal uses hidden state Markov models in conjunction with recursive formulations of robust decision making. Concerns about robustness apply both to the specification of the underlying dynamics and to the estimation of the hidden growth states.
Second, the economic values of assets that have important payout components far into the future incorporate long-run notions of risk or uncertainty. Operator methods will be applied to Markov environments. These methods give ways to infer long-run consequences from the transition dynamics of underlying state variables in an economy. In the proposed research, these methods will be tailored to the study of the long run components of asset values. Valuation operators link prices of payoffs with different maturities. A specific valuation operator maps investment payoffs in the future into current values. A family of such operators can be constructed depending on the time between the payoff and the current value. These valuation operators may be well approximated by a small number of components or even a single component when the elapsed time between the payoff date and the valuation date is large. For instance, a dominant component or eigen function may exist that dictates how values are related to payoffs in the long run. These operator methods applied to possibly nonlinear Markov environments give rise to well defined notions of dominant pricing factors and well defined ways to characterize when these components are important. These operator methods give measures of the long-run components of asset values implied by dynamic economic models. While these methods are applicable more generally, in the proposed research particular attention will be given to the class of economic models that feature long-run components of uncertainty.
Third, decision-makers may smooth information when taking actions because of costs or constraints on the flow of information. This research explores what implications these information flow constraints have for dynamic economic models with growth uncertainty. Smooth predictions of hidden states may be less costly to process. Results from information theory suggest that this mechanism provides a useful perspective on the role of signals in Markov decision problems. Signal processing can emerge as the outcome of optimization subject to information constraints. Economists have found this to be an intriguing model of why economic agents respond sluggishly to information.
