OPTIMAL SIMPLE FISCAL RULES 5 that government can choose the _untargeted_ fiscal rule to be fairly similar to the rule they would like to target at the HtM HHs. This rule is similar to the one that maximizes HtM HH welfare, _conditional_ on transfers being untargeted.

**Relation to literature** As discussed above, most recent quantitative models of fiscal rules for commodity exporters have argued that commodity revenues should be saved, and balanced budget rules are suboptimal. To our knowledge, there are no recent papers that challenge that view. While it has been known for some time that (i) commodity prices are close to a random walk, and (ii) permanent changes in income should be spent (for example, see Basch and Engel 1993), researchers have generally avoided incorporating highly persistent shocks into quantitative models of optimal fiscal rules. This has led to the current consensus in favor of saving commodity revenues.<sup>8</sup>

Our results are related to several papers which treat commodity price shocks as highly persistent, though none of these papers calculate optimal fiscal rules. First, our findings are consistent with the policy discussion in Cashin _et al_ (2000), who argue that highly persistent commodity price shocks are likely to undermine commodity price stabilization schemes. Cashin _et al_ (2000) focus on estimating the persistence of commodity prices and make their policy argument descriptively, rather than calculating the welfare consequences of different rules as we do here. Second, our results are related to JS2016. Although our results are consistent with theirs (suitably modified to a consistent framework as discussed above and in Section 5), JS2016 evaluate optimal reserve management rather than optimal fiscal rules and do not include Hand-to-Mouth (liquidity constrained) households. Finally, Fornero and Kirchner (2014) decompose copper prices into temporary and persistent components and find that the latter is highly persistent. They build a New Keynesian model where agents learn about the true persistence of commodity prices, and show impulse re— sponses to persistent commodity price shocks under different fiscal rules although they don’t calculate the welfare consequences of those different rules.

— Naturally, there are a number of important real world issues we have abstracted from such as irreversible public investment and political constraints — which are discussed in the conclusion. Nonetheless, our paper does clarify that if a structural surplus rule is optimal, it should be justified along those lines, rather than in order to smooth consumption of constrained households.

**Structure of the paper** Our paper is organized as follows. In Section 2, we solve for the optimal simple rule analytically in a model with only hand-to-mouth (liquidity constrained) households. In Section 3 we present our main quantitative model, which includes two types of households but where output and commodity prices are exogenous. In Section 4 we present the main numerical results in terms of the welfare loss under different popular fiscal rules, and also the optimal fiscal rule. We then present three extensions to the baseline model. In Section 5 we show that the linear model of Section 4 comes close to replicating the optimal policy in the non-linear model of

> 8Other researchers have modeled government spending as not valued by households, such as Garcia-Cicco and Kawamura (2015). BJS2013 and Bems and de Carvalo Filho (2011) consider the welfare gains of hedging and the role of precautionary savings in models where commodity exporters face persistent commodity price shocks, but neither paper discusses fiscal rules.