OPTIMAL SIMPLE FISCAL RULES 26 Table 5. Welfare Properties of Optimal Rules - Spillovers from Commodity Prices to Non-Resource GDP.

|_βY P_ = 0_._2<br>_ψ_ = 0_._01|(1) BBR|**(A) C**<br>(2) BBR#|**lassical Ru**<br>(3) SSR<br>|**les** (_σy_ = 0_._04)<br>(4) BBR-CCY|(5) SSR-CCY|**(B) OSR-E**<br>(6) Optimal|**qual** (_σy_ = 0_._04)<br>(7) _θy_ **=**-0.5 fxed|**(C) OSR-E**<br>(8) Optimal|**qual** (_σy_ = 0_._22)<br>(9) _θy_ **=**-0.5 fxed|
|---|---|---|---|---|---|---|---|---|---|
|_θa_|0.10|0.10|0.10|0.10|0.10|0.09|0.09|0.09|0.09|
|_θy_|0.15|0|0.00|-0.85|-0.85|-0.80|-0.50|-0.77|-0.50|
|_θp_|1.00|1.00|0.00|1.00|0.00|1.06|0.88|1.04|0.88|
|_sd_(ˆ_c_<sup>_′_</sup>)|0.25|0.25|0.25|0.25|0.25|0.25|0.25|0.25|0.25|
|_sd_(ˆ_c_<sup>_′′_</sup>)|0.26|0.26|0.26|0.25|0.29|0.25|0.25|0.25|0.25|
|_sd_( ̃_a_)<br>|0.05|0.19|2.67|1.46|3.94|1.45|1.44|1.59|1.52|
|_sd_(<sup> ̃</sup>_b_)|2.51|2.15|1.81|0.14|3.82|0.28|0.28|0.33|0.31|
|**Loss**|6.54|6.41|6.49|6.10|7.49|6.09|6.09|6.31|6.42|
|_ρyp_|||0.96||||0.96||0.50|
|_ρyt,yt−_1|||0.85||||0.85||0.23|

<u>#</u> Balance Budget Rule which doesn’t respond to tax revenues. Fiscal rule coefficients are the same for both households.

# 7. Extension 3: Real Business Cycle model

In the models of Sections 4-6 we assumed that non-resource GDP is exogenous. In this section, we set up a small open economy (SOE) real business cycle (RBC) model and show that our main results are robust in a model with _endogenous_ output in the non-resource sector.

**Model Overview** . The SOE RBC model maintains the basic structure of the exogenous-income — model of the Section 4 two types of households, exogenous commodity income, a debt-elastic — interest rate spread and fiscal rules based on transfers to HHs but introduces endogenous capital accumulation, labor supply and production in the non-resource sector of the economy. Output in this sector is produced by competitive firms by combining labor hired from both types of households and capital rented from the Ricardian HH (HtM HHs don’t own capital) using a Cobb-Douglas production technology. Volatility in non-resource GDP is driven by temporary TFP shocks ( _ρz_ = 0). As is standard in the SOE literature, we assume GHH preferences which imply that labor supply is unaffected by variations in household wealth.<sup>29</sup> The capital share of income is _α_ = 1 _/_ 3, and the Frisch elasticity of labor supply is ( _η −_ 1)<sup>_−_1</sup> = 2 _._ 2 (see Appendix D.1 for further details on the calibration and a description of the RBC model).

There are two main changes in the RBC model relative to the exogenous income model: the endogeneity of labor and the endogeneity of capital. To isolate each of these effects we first add endogenous labor in Panel A of Table 6 keeping the capital stock fixed at its steady state level (by assuming very high capital adjustment costs). Then in Panel B, we allow both labor and capital to vary. For all the results in Table 6 we also fix _θA_ = 0 _._ 1, which simplifies the exposition but usually has little effect on welfare (see the end of this section for a further discussion).

**Endogenous labor supply (and fixed capital)** The RBC model with fixed capital has very similar optimal rules as the exogenous income model without spillovers, allowing for some scaling of the coefficient on non-resource GDP. In Table 6, Panel A Column 1 we present OSR-Equal, when instead of responding to non-resource GDP, the fiscal rule responds to the fundamental TFP

> 29This is an important assumption. With standard (separable) preferences, an increase in commodity prices would cause households to want to consume more leisure, reducing labor supply and GDP. This would be contrary to the evidence presented above that GDP and commodity prices are generally positively correlated for commodity exporters.