*7.1. Political Planner*

In this example, consumers are assumed to have arbitrarily distorted—skeptical beliefs about the approximating scientific model *π*, as described in Section 2.1. Importantly, the government is ignorant of these beliefs. The reason for its ignorance is fundamental: as noted by Hansen and Sargent (2012), the government's ambiguity arises because the possible space of models that are unknown to the fiscal planner but known to the consumer is so vast that it is impossible to infer the private sector's probability model from finite data, providing a motive to construct robust climate and fiscal policies by solving a socalled multiplier problem that protects against worst-case belief distortions. As Hansen and Sargent (2012) put it, the government's ignorance of private beliefs is akin to a set or cloud of probability distributions over events *x* centered on the reference or approximating density *π* constrained by a discounted relative entropy set of probability distributions reflecting the unknown beliefs of the private sector.25 Its ignorance notwithstanding, this political planner acts under the assumption that the unknown beliefs are true.

With this in mind, the recursion (46) becomes

$$\begin{split} \mathcal{W}\_{t}(\mathbf{Y}\_{t},k\_{t},\mathbf{Q}\_{t}) &= \max\_{\boldsymbol{c}\_{t},\boldsymbol{E}\_{t},\mathbf{k}\_{t+1},\mathbf{Q}\_{t+1},\mathbf{Y}\_{t+1}} \min\_{\boldsymbol{n}\_{t+1}} u(\mathbf{c}\_{t}) - \frac{\beta}{\sigma} \mathbb{E}\_{t} n\_{t+1} \log n\_{t+1} \\ &+ \quad \beta \mathbb{E}\_{t} n\_{t+1} \mathcal{V}\_{t+1}(\mathbf{Y}\_{t+1},k\_{t+1},\mathbf{Q}\_{t+1}) \\ &+ \quad \Phi\_{t} [\boldsymbol{\Omega}\_{t} + \mathbb{E}\_{t} n\_{t+1} \mathbf{Y}\_{t+1} - \mathbf{Y}\_{t}] + \mathcal{M}\_{t}. \end{split} \tag{47}$$

The political government's acceptance of private-sector beliefs *Mt* as true means that *mt*+1, which multiplies Υ*t*+<sup>1</sup> in the implementability constraint, is set equal to *nt*+1—the authority adopts the consumer's distortion as its own.26 Ambiguity is activated with the entropy constraint penalizing deviations of distorted beliefs from true beliefs (1), where − 1 *<sup>σ</sup>* is a Lagrangian multiplier, and *σ* < 0 measures the planner's ambiguity aversion. As *σ* moves toward −∞, the government's preference for robustness rises. As *σ* approaches a break-down *σ* < 0 from above, the government's concern about distortions to expectations is maximal. Conversely, as *σ* approaches zero, the government's preference for robustness diminishes, until, in the limit the government fully adopts the approximating reference model as true and not subject to doubt.
