OPTIMAL SIMPLE FISCAL RULES 4 this, and derive optimal precautionary holdings of reserves (equivalent to an SWF). Since our main results rely on a linear model, it is natural to ask if we are overestimating the pro-cyclicality of optimal fiscal rules because we abstract from non-linear constraints. In fact, JS2016 find that an optimal simple linear rule similar to the one used in this paper is able to deliver the vast majority of the welfare gains from optimal non-linear reserve management. It turns out that our simple linear model is able to capture much of the dynamics of precautionary savings in JS2016 when we increase the debt-elastic interest spread. When we choose the debt-elastic interest spread to match the autocorrelation of net assets/reserves in JS2016 (with their calibration) we find almost exactly — the same degree of pro-cyclicality of the fiscal rule as well as the first-order autocorrelation — of the trade balance-to-output ratio observed in the data even though neither of these were calibration targets. When we use that debt-elasticity with our default calibration, we find that it actually _increases_ the fraction of above-average commodity revenues that are spent. These results suggest that (i) our simple linear model with a reduced form financial friction is able to capture much of the dynamics of more complicated non-linear models, and (ii) if anything our simple linear model _understates_ the pro-cyclicality of optimal fiscal rules.

**Commodity price spillovers and endogenous GDP** Another real-world concern is that in commodity intensive economies, shocks to commodity prices spill over into the non-resource economy, potentially complicating the optimal simple rule and motivating greater smoothing of commodity price shocks. In two extensions, first with exogenous spillovers and second in a real business cycle (RBC) model, we show that actually spillovers make the variation in the non-resource economy more persistent, which _increases_ the pro-cyclicality of the optimal fiscal rule with respect to commodity revenues. In these economies, the optimal rule involves spending _all_ of commodity — — revenues as these are the ultimate cause of the increase in persistence in non-resource GDP but still responding counter-cyclically to temporary non-resource GDP shocks as before.

**Government objectives, untargeted transfers and an irrelevance result** As there are two types of households, the government might care more about some households than others. For example, the government might care more about the welfare of HtM HHs because they are poorer.<sup>7</sup> In the extreme case that the government _only_ cares about HtM HHs, it possible to completely insure HtM HHs from all risk, though this results in large welfare losses for the Ricardian (unconstrained) HH, and so some risk sharing across households is generally optimal if the government cares about the welfare of both households.

Although the government might be able to target transfers to particular groups, it is unlikely that they would be able to do so perfectly. Practically, this is not a huge problem, because Ricardian households are indifferent to changes in the timing of transfers, so long as their present value remains the same. In the paper, we show that under some conditions, the fiscal rule followed will be _irrelevant_ for Ricardian HH consumption and welfare. Even if those strict conditions are not met, Ricardian HHs welfare is fairly insensitive to many changes in fiscal rules, which means 7In our main results, we assume that all households have the same per capita income and their weights in the government’s social welfare function are equal. Alternatively, if HtM households were poorer, then a utilitarian government would automatically put more weight on minimizing volatility in their consumption.