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Asset prices and the equity premium might reflect doubts and pessimism. Introducing these features in an otherwise standard New-Keynesian model changes optimal policy in a substantial way. There are three main results: (i) asset-price movements improve the inflation-output trade-off so that average output can rise without much inflation costs; (ii) a “paternalistic” policymaker – maximizing the expected utility of the consumers under the true probability distribution – chooses a more accommodating policy towards productivity shocks and inflates the equity premium; (iii) a “benevolent” policymaker – maximizing the objective through which decisionmakers act in their ambiguous world – follows a policy of price stability.

After the 2007–2009 financial crisis, some argued that monetary policy had been too expansionary fuelling an asset price bubble.1 This paper revisits the theme of monetary policy and asset prices in a standard New-Keynesian monetary model. An important shortcoming of current models is to have counterfactual implications for the equity premium and other financial relationships. This issue is addressed by introducing distortions in agents׳ beliefs– doubts and ambiguity aversion – which enable the model to reproduce realistic values for the equity premium and the market price of risk.2 The focus of this work is to study how the presence of doubts and ambiguity influences the characterization of optimal monetary policy. In our framework, agents do not trust the true probability distribution and make robust choices using a distorted probability distribution. In this environment, the objective of a policymaker caring about the agents might not be uniquely defined. This paper distinguishes between a “paternalistic” policymaker who cares about the utility of agents evaluated under the true probability distribution, and a “benevolent” policymaker who maximizes the objective through which agents handle their decisions in their ambiguous world. The policy conclusions change in a substantial and interesting way with respect to the rational-expectations model, when the policymaker is paternalistic, while they do not change for the benevolent policymaker. With rational expectations, the welfare-maximizing policy following a productivity shock requires price stability. Moreover, average output cannot rise because it is too costly to increase inflation and therefore price dispersion.3 In our framework, the welfare-maximizing policy of the paternalistic policymaker is more accommodating and involves an increase in inflation following positive productivity shocks. Distorted beliefs enter the stochastic discount factor. This creates a wedge between average real marginal costs (or average output) and average inflation. The wedge is driven by the co-movements between the stochastic discount factor and the real marginal costs. Since the stochastic discount factor is negatively related to long-run productivity, it is countercyclical. If real marginal costs are procyclical, as following accommodating policies, average output can increase without much rise in average inflation and price dispersion. The side effect of this optimal policy is the increase in the volatility of quantities and a larger equity premium. When the policymaker is instead benevolent, two forces balance out to deliver price stability as the optimal policy. One pointing towards a more procyclical policy response through the channel described above, and the other towards a countercyclical policy because now ambiguity enters directly into the welfare objective of the policymaker. Moreover, this paper shows that an interest rate rule calibrated to match monetary policy under Greenspan׳s tenure as a chairman of the Federal Reserve achieves equilibrium allocations that resemble the ones prescribed by optimal policy of the paternalistic policymaker in our framework. Greenspan׳s policy is closer to optimal policy in our model than the traditional Taylor rule. In fact, in our model, exploiting the less severe output-inflation trade-off requires a relatively more procyclical policy. However, the estimated Greenspan׳s policy is found to be too accommodative even from the perspective of our model. The closest paper to our work is Karantounias (2013a), which analyzes a Ramsey problem but in the optimal taxation literature where, like in our paternalistic policymaker׳s case, the private sector distrusts the probability distribution of the model while the government fully trusts it. Our paper also analyzes a benevolent policymaker case.4 Woodford (2010a) studies an optimal monetary policy problem in which the monetary policymaker trusts its own model but not its knowledge of the private agents׳ beliefs. In our context, it is only the private sector that has doubts on the true model whereas the policymaker is fully knowledgeable even with respect to the doubts of the private sector. The different framework of Woodford (2010a) implies, in contrast to our results, that the optimal stabilization policy following productivity shocks is to keep prices stable no matter what is the degree of distrust that the agents might have.5Dupor (2005) analyzes optimal monetary policy in a New-Keynesian model in which only the investment decisions are distorted by an ad hoc irrational expectational shock. In our framework, the distortions in the beliefs are instead the result of the aversion to model misspecification on the side of households, which also affects in an important way the intertemporal pricing decisions of the firms on top of the investment decisions. There are several other papers that have formulated optimal monetary policy in ad hoc linear-quadratic framework where the other main difference with respect to our work is that the monetary policymaker distrusts the true probability distribution and the private-sector expectations are aligned with that distrust.6 The structure of the paper is the following. Section 2 presents the model. Section 3 describes the monetary policy problem. Section 4 characterizes the optimal policy. Section 5 studies the mechanism through which doubts and ambiguity matter for policy. Section 6 compares optimal policy with interest-rate rules. Section 7 concludes.

Doubts are introduced into a standard New-Keynesian monetary model. In our model, households express distrust regarding the true probability distribution. These doubts are reflected in asset prices and might generate, together with ambiguity aversion, equity premia of similar size as those found in the data. This is an important feature of our framework with respect to the benchmark model, which, on the contrary, is unable to match asset-price data. In this environment optimal policy is studied from the perspective of two policymakers: a benevolent policymaker who cares about the utility through which agents act and a paternalistic policymaker who instead cares about the utility agents would have if they were not dubbing the model. Results change in a substantial way with respect to the benchmark model when the policymaker is paternalistic. A standard finding of the literature is the optimality of a policy of price stability following productivity shocks. In our model with doubts, a paternalistic policymaker should have a more procyclical policy response with respect to productivity shocks, inflating the equity premium. The larger the departure, the higher is the degree of distrust that agents have. Instead, a benevolent policymaker would get close to the optimal policy of the benchmark model since in this case distorted beliefs have only second-order effects. Indeed, the distorted beliefs in the objective function of the policymaker are aligned with those in the forward-looking private-sector reaction functions. There are several limitations of our modeling strategy. First, households and firms share the same degree of doubts. Households׳ doubts are reflected in Arrow–Debreu prices and those are used to evaluate both the asset prices and the future profits of the firms. Results can change if within the private sector there are different degrees of doubts on the model. Second, the only disturbance affecting the economy is a productivity shock. Results would not change with stationary markup shocks. Indeed, doubts and ambiguity aversion are reflected in fears of bad news regarding long-run consumption on which transitory markup shocks, contrary to persistent productivity shocks, do not have much influence. Third, an interesting case to analyze is one in which the policymaker distrusts the reference probability distribution with a different degree of ambiguity than the private sector. However, along these lines, the optimal policy of our paternalistic policymaker would be interpreted as that of a policymaker who completely trusts the model while the optimal policy of the benevolent policymaker would be interpreted as that of a policymaker who has the same degree of distrust as the private sector. The analysis of the intermediate cases is left to future work. Finally, we have abstracted from credit frictions and asset-market segmentation, which can be important features to add to properly model asset prices and the transmission mechanism of shocks. This is also material for future works. Here, the analysis is kept the closest as possible to the benchmark New-Keynesian model to show how a small departure from that model delivers important differences in the policy conclusions and how this departure can rationalize a too accommodative monetary policy as an optimal policy following productivity shocks.