OPTIMAL SIMPLE FISCAL RULES 23 and Tobago and Garcia-Cicco _et al_ (2010) estimate 0.58 for Argentina and 0.62 for Mexico (Figure 3 Panel A).

Table 4 shows the welfare performance of optimal and classical rules when we use the higher debt-elastic interest spread consistent with JS2016 ( _ψ_ = 0 _._ 45), but applied to the baseline calibration which has higher commodity price persistence ( _ρp_ = 0 _._ 93). Column 6 shows that adding a debt-elastic interest rate spread makes the OSR-Equal significantly _more procyclical_ than the baseline case with low _ψ_ . Most important, the government spends 77% of above-average commodity revenues here against 68% in the baseline in Table 2. Because more higher debt-elastic of interest rates make deviations of public assets from their long-run level more costly, the speed of convergence of public assets towards the target is much faster relative to the baseline case ( _θa_ = 0 _._ 31 vs _θa_ = 0 _._ 09 in the baseline). Column 5 also shows that the targeted optimal simple rule is more procyclical relative to the baseline calibration and columns 1-4 show that the welfare gains of adopting a BBR (relative to SSR) increase with _ψ_ .

In sum, we find that (i) the linear model of Section 4 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 baseline simple linear model _slightly understates_ the optimal pro-cyclicality of fiscal rules.

Table 4. Fiscal Rule with _<u>ψ</u>_ to capture <u>precautionary</u> savings.

|_ψ_ = 0_._45|(1)|(2)|(3)|(4)|(5)|(6)|
|---|---|---|---|---|---|---|
|_ρP_ = 0_._93|**BBR**|**SSR**|**BBR CCY**|**SSR CCY**|**OSR**|**OSR Equal**|
|_θ_<sup>_′_</sup><br>_a_|0.10|0.10|0.10|0.10|0.46|0.31|
|_θ_<sup>_′_</sup><br>_y_|0.15|0.00|-0.85|-0.85|-0.60|-0.60|
|_θ_<sup>_′_</sup><br>_p_|1.00|0.00|1.00|0.00|0.61|0.77|
|_θ_<sup>_′′_</sup><br>_a_|0.10|0.10|0.10|0.10|0.26|0.31|
|_θ_<sup>_′′_</sup><br>_y_|0.15|0.00|-0.85|-0.85|-0.60|-0.60|
|_θ_<sup>_′′_</sup><br>_p_|1.00|0.00|1.00|0.00|0.74|0.77|
|_sd_(ˆ_c_<sup>_′_</sup>)|0.16|0.22|0.16|0.22|0.16|0.16|
|_sd_(ˆ_c_<sup>_′′_</sup>)|0.16|0.18|0.16|0.18|0.15|0.16|
|_sd_( ̃_a_)|0.07|2.37|0.12|2.37|0.19|0.15|
|_sd_(<sup> ̃</sup>_b_)|0.20|4.61|0.25|4.61|0.27|0.20|
|**Loss (% of** _Css_**)**|2.54|4.02|2.51|4.01|2.48|2.48|

# 6. Extension 2: Spillovers from Commodity Prices to non-resource GDP

In commodity exporting countries, changes in commodity prices often have a large impact on GDP. In both Trinidad & Tobago and Algeria, real GDP per capita rose as oil prices increased in the 1970s and early 1980s, fell during the period of low oil prices from the mid-1980s, and then growth returned as oil prices increased from around 2000 (Figure 6).<sup>24</sup> After detrending both series, the correlation between log real GDP and log real oil prices is around 0.5 for Trinidad & 24 Ideally one would like to use non-resource GDP per capita, rather than GDP per capita, which of course includes oil and gas production. As GDP is in real terms, there should not be any mechanical effect of commodity prices on output. Moreover, oil and gas production are known to be fairly inelastic to oil price movements in the short term, given the large fixed costs of oil and gas production.