OPTIMAL SIMPLE FISCAL RULES 31

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# Appendix A. The Persistence of Commodity Price Shocks

The persistence and volatility of the price shocks are calibrated to different commodity prices, reported in Table 7. We estimate an AR(1) process for the natural log of real prices of beef, coffee (Robusta), soy beans, bananas and coffee (Arabica) using annual data from World Bank’s “Pink Sheet” on commodity prices.<sup>36</sup> We complement our estimates with those of BJS2013 who use commodity price data from the International Finance Statistics (IFS) to estimate the persistence of petroleum, copper, gold and sugar. For the sake of comparison, we report the estimates in Cashin _et al_ (2000) (their Table 3) in the last column. They estimate the persistence of the commodity price shocks using monthly IMF data between 1957-1998 and a median-unbiased estimator, including — a time trend. One can see that for most commodities and especially the most persistent commodities — our estimates of persistence are generally lower than those in Cashin _et al_ (2000).<sup>37</sup> This means that, if anything, our estimates of the optimal fiscal rule are not pro-cyclical enough.

Table 7. Calibration of Commodity Price Persistence (in years)

||**Persistence**|**Half Life**|OSR<br>_θp_|**Source**|**Sample**|**Half**<br><1|**Life **<br>1-4|**from**<br>5-8|**Cash**<br>9-18|**in et al**<br>_∞_|
|---|---|---|---|---|---|---|---|---|---|---|
|Petroleum|0.94|11.2|0.73|IFS/BJS(2013)|1970–2008|||||X|
|Beef|0.90|6.6|0.56|WB PinkSheet|1960-2016|||X|||
|Natural Gas|0.89|6|0.53|IFS/BJS(2013)|1985–2008|||||X|
|Copper|0.89|6|0.53|IFS/BJS(2013)|1957–2008|||X|||
|Gold|0.89|6|0.53|IFS/BJS(2013)|1970–2008|||||X|
|Cofee (Robusta)|0.89|6|0.53|WB PinkSheet|1960-2016|||||X|
|Soy Beans|0.87|5|0.48|WB PinkSheet|1960-2016||X||||
|Bananas|0.80|3|0.35|WB PinkSheet|1960-2016|X|||||
|Cofee (Arabica)|0.77|2.6|0.31|WB PinkSheet|1960-2016||||X||
|Sugar|0.74|2.3|0.28|IFS/BJS(2013)|-||||X||

> 36The estimates in Table 7 do not include a time trend, because (if taken literally) this would imply that _real_ log prices would go to _∞_ or zero in the (very) long run, neither of which are feasible.

> 37This is unsurprising as Cashin _et al_ (2000) argue that least squares estimates of persistence are downward biased.