Woodford's approach to robust policy analysis in a linear-quadratic framework

This paper extends Woodford's approach to the robustly optimal monetary policy to a general linear quadratic framework. We provide algorithms to solve for a time-invariant linear robustly optimal policy in a timeless perspective and for a time-invariant linear Markov perfect equilibrium under discretion. We apply our methods to a New Keynesian model of monetary policy with persistent cost-push shocks and inflation persistence. We find that the robustly optimal commitment inflation is less responsive to a cost-push shock when the shock is more persistent and that the robustly optimal discretionary policy is more responsive to lagged inflation when inflation is more persistent.Accepted manuscrip

Ambiguity in asset pricing and portfolio choice: a review of the literature

A growing body of empirical evidence suggests that investors’ behavior is not well described by the traditional paradigm of (subjective) expected utility maximization under rational expectations. A literature has arisen that models agents whose choices are consistent with models that are less restrictive than the standard subjective expected utility framework. In this paper we conduct a survey of the existing literature that has explored the implications of decision-making under ambiguity for financial market outcomes, such as portfolio choice and equilibrium asset prices. We conclude that the ambiguity literature has led to a number of significant advances in our ability to rationalize empirical features of asset returns and portfolio decisions, such as the empirical failure of the two-fund separation theorem in portfolio decisions, the modest exposure to risky securities observed for a majority of investors, the home equity preference in international portfolio diversification, the excess volatility of asset returns, the equity premium and the risk-free rate puzzles, and the occurrence of trading break-downs.Capital assets pricing model ; Investments

Ambiguity, Learning, and Asset Returns

We propose a novel generalized recursive smooth ambiguity model which allows a three-way separation among risk aversion, ambiguity aversion, and intertemporal substitution. We apply this utility to a consumption-based asset pricing model in which consumption and dividends follow hidden Markov regime-switching processes. Our calibrated model can match the mean equity premium, the mean riskfree rate, and the volatility of the equity premium observed in the data. In addition, our model can generate a variety of dynamic asset pricing phenomena, including the procyclical variation of price-dividend ratios, the countercyclical variation of equity premia and equity volatility, and the mean reversion of excess returns. The key intuition is that an ambiguity averse agent behaves pessimistically by attaching more weight to the pricing kernel in bad times when his continuation values are low.Ambiguity aversion; learning; asset pricing puzzles; model uncertainty; robustness; pessimism

Robust Equilibrium Yield Curves

This paper studies the quantitative implications of the interaction between robust control and stochastic volatility for key asset pricing phenomena. We present an equilibrium term structure model in which output growth is conditionally heteroskedastic. The agent does not know the true model of the economy and chooses optimal policies that are robust to model misspecification. The choice of robust policies greatly amplifies the effect of conditional heteroskedasticity in consumption growth, improving the model's ability to explain asset prices. In a robust control framework, stochastic volatility in consumption growth generates both a state-dependent market price of model uncertainty and a stochastic market price of risk. We estimate the model using data from the bond and equity market, as well as consumtion data. We show that the model is consistent with key empirical regularities that characterize the bond and equity markets. We also characterize empirically the set of models the robust representative agent entertains, and show that this set is "small". In other words, it is statistically difficult to distinguish between models in this set.Yield curve, market price of uncertainty, robust control

Multi-Source Neural Variational Inference

Learning from multiple sources of information is an important problem in machine-learning research. The key challenges are learning representations and formulating inference methods that take into account the complementarity and redundancy of various information sources. In this paper we formulate a variational autoencoder based multi-source learning framework in which each encoder is conditioned on a different information source. This allows us to relate the sources via the shared latent variables by computing divergence measures between individual source's posterior approximations. We explore a variety of options to learn these encoders and to integrate the beliefs they compute into a consistent posterior approximation. We visualise learned beliefs on a toy dataset and evaluate our methods for learning shared representations and structured output prediction, showing trade-offs of learning separate encoders for each information source. Furthermore, we demonstrate how conflict detection and redundancy can increase robustness of inference in a multi-source setting.Comment: AAAI 2019, Association for the Advancement of Artificial Intelligence (AAAI) 201

Robust Equilibrium Yield Curves

This paper studies the quantitative implications of the interaction between robust control and stochastic volatility for key asset pricing phenomena. We present an equilibrium term structure model with a representative agent and an output growth process that is conditionally heteroskedastic. The agent does not know the true model of the economy and chooses optimal policies that are robust to model misspecification. The choice of robust policies greatly amplifies the effect of conditional heteroskedasticity in consumption growth, improving the model’s ability to explain asset prices. In a robust control framework, stochastic volatility in consumption growth generates both a state-dependent market price of model uncertainty and a stochastic market price of risk. We estimate the model using data from the bond and equity markets, as well as consumption data. We show that the model is consistent with key empirical regularities that characterize the bond and equity markets. We also characterize empirically the set of models the robust representative agent entertains, and show that this set is ?small?. That is, it is statistically difficult to distinguish between models in this set.Yield curves, Market price of Uncertainty, Robust control.

Robustness and macroeconomic policy

This paper considers the design of macroeconomic policies in the face of uncertainty. In recent years, several economists have advocated that when policymakers are uncertain about the environment they face and find it difficult to assign precise probabilities to the alternative scenarios that may characterize this environment, they should design policies to be robust in the sense that they minimize the worstcase loss these policies could ever impose. I review and evaluate the objections cited by critics of this approach. I further argue that, contrary to what some have inferred, concern about worst-case scenarios does not always lead to policies that respond more aggressively to incoming news than the optimal policy would respond absent any uncertainty.Macroeconomics - Econometric models

Confidence and ambiguity

This paper proposes a model of the decision-maker’s confidence in his probability judgements, in terms of an implausibility measure – a real-valued function on the set of probability functions. A decision rule is axiomatised according to which the decision-maker evaluates acts using sets of probability functions which vary depending on the agent’s implausibility measure and on what is at stake in the choice of the act. The framework proposed yields a natural notion of comparative aversion to lack of confidence, or ambiguity aversion, and allows the definition of an ambiguity premium. It is shown that these notions are equivalent and can be characterised in terms of the implausibility measure representing the agent’s confidence. A simple portfolio example is presented.Confidence; multiple priors; ambiguity aversion; ambiguity premium; implausibility measure