OPTIMAL SIMPLE FISCAL RULES 21 Table 3. The Role of Precautionary Savings: Calibration and OSR in Linear and Non- <u>Linear Models.</u>

||**symbol**|**Exogenous Income Model**<br>(Linear Model of Section 4)|**Jeanne and Sandri (2016)**<br>(Global Fully Optimal)|
|---|---|---|---|
|**Panel A: Calibration**||||
|Coefcient of risk aversion|_σ_|2|2|
|Elasticity of substitution (imports/nontradables)|_η_|_∞_|1|
|Annual persistence of real interest rates|_ρr_|0|0.19|
|Annual std. dev of real interest shocks|_σr_|0|0.13|
|Annual persistence of commodity revenues|_ρp_|0.78|0.78|
|Annual std. dev of commodity revenues shocks|_σp_|16%|16%|
|Tax rate|_τ_|0%|0%|
|Intertemporal discount factor|_β_|0.951|0.99|
|Long-run growth rate|_G_|0%|4.6%|
|Long-run transfers (share of annual non-res GDP)*|_Trss_|33%|–|
|Debt-elasticity of country premia**|_ψ_|0.45|–|
|**Panel B: Calibration Targets**||||
|Long-run real interest rate|_rss_|5.1%|5.1%|
|1st order autocorrelation of assets (public + private)|_ρabt,abt−_1|0.81|0.8|
|Long-run SWF/Reserves (share of annual imports)|_Ass/Mss_|22%|22%|
|**Panel C: Untargeted Moments and OSR**||||
|1st order autocorrelation of trade balance-to-output ratio|_ρtb_|0.55***|–|
|Optimal change in transfers given a $1 increase in SWF|_θa_|**0.33**|**0.24**|
|Optimal change in transfers given a $1 increase in commodity revenues|_θp_|**0.67**|**0.65**|

*Calibrated to match the estimated optimal long-run target of reserves in JS2016. **Calibrated to match the 1st order autocorrelation of foreign reserves in JS2016. *** Our estimates of the 1st autocorrelation of the trade balance-to-output ratio for Algeria and T&T are 0.52 and 0.56 respectively.

**Comparing the exogenous income model with JS2016.** In this section, we increase the debt-elastic spread _ψ_ until our model is able to replicate the first-order autocorrelation of net assets/reserves (public+private) in JS2016 with the OSR-Equal fiscal rule with the same calibration. We then check if the linear model of section 4 is biased towards more procyclical rules by comparing our rule with that in JS2016, and re-generating Table 2 with the higher value of _ψ_ . But before we do this we need to recalibrate the predetermined parameters of our model so that they are in line with JS2016.

Panel A of Table 3 shows the calibration of key parameters in JS2016 and the new calibration (aimed to “mimic” JS2016) of the linear exogenous income model of section 4.<sup>22</sup> Note that the estimated persistence of the value of exports ( _ρp_ = 0 _._ 78) is significantly lower than our baseline estimate for Algeria and Trinidad & Tobago ( _ρp_ = 0 _._ 93). We set _τ_ = 0 since there are no taxes in JS2016. We lowered the intertemporal discount factor ( _β_ = 0 _._ 95) and steady-state transfers ( _Trss_ = 0 _._ 33) to match the long-run interest rate ( _rss_ = 5 _._ 1%) and the optimal level of reserves ( _Ass/Mss_ = _._ 22 _∼_ 2.2 months of imports) in JS2016, respectively (shown in Table 3 Panel B).<sup>23</sup>

> 22JS2016 use annual data from a group of 24 developing countries (sample 1960 to 2014) provided by the World Bank’s World Development Indicators to calibrate the path of detrended non-tradable output, value of exports and the country’s interest rate.

> 23Under the new calibration (aside from discrepancies generated by the linearity assumption) there are two main differences between the models: the elasticity of substitution between non-tradable and imported goods and the structure of the country’s interest rates. In the exogenous income model, we implicitly assume that imported goods and non-tradable goods are perfect substitutes _η_ = _∞_ . Second, the country’s interest rate path is assumed to follow an AR(1) process in JS2016. In our model, the interest rate depends on the country’s net debt, and its persistence