# **7. The Bounds Test Sheets**

Bounds tests are used to assess the behavior of the public debt ratio under different assumptions on key parameters. Shocks equal to 2 standard deviations with respect to the 10-year historical averages during the first two years of the projection period are applied separately to the real interest and growth rates, and the primary balance, respectively. The template also examines debt trajectories in the case of a 30 percent real depreciation of the local currency and a contingent liabilities shock of 10 percent of GDP. The latter is presented as a rough measurement of an increase in debt- creating flows, given the difficulties in discussing contingent liabilities risk.<sup>12</sup> In addition, a combined shock of 1 standard deviation with respect to historical averages of these variables for the first two years of the projection period is also reported. The magnitude of shocks to individual variables is consistent with shocks that have typically been observed in the run-up to a crisis. In the same way, the combined shock is consistent with the historical evidence that such shocks do not happen in isolation, but occur simultaneously.<sup>13</sup> In all bounds tests, variables revert to the baseline projection after two years.<sup>14</sup> It is important to emphasize that these tests do not represent full-fledged scenarios, as there is no interaction among variables. More specifically, the stress tests are built by replacing in the baseline projections the value of one variable (for instance, the interest rate), leaving all other variables unchanged, with only a few exceptions: (i) interest payments on debt are endogenous, i.e., they increase in scenarios where interest rates are higher; (ii) public sector revenues are endogenous with respect to GDP: shocks in the latter also affect revenue; and, of course, (iii) the debt stocks are endogenous. But the remaining parameters are left mostly unchanged: for example, in the stress tests featuring a shock to GDP, the real exchange rate remains unchanged.

Each bounds test is calculated in a different sheet, which presents the debt decomposition table and the gross financing needs modified according to the simulated shock. Variables modified in the bounds tests are highlighted in red as in the case of the alternative scenarios.

## 1) Shock to the Real Interest Rate

This shock is represented in sheet “B1_Irate”. The real interest rates on domestic and foreign debt are supposed to be equal to their historical average plus 2 standard deviations for the first and second year of projections, respectively. The real interest rates return as in the baseline in the following years (cells O49:P55, Table 9).

> 12 This issue was discussed in detail in SM/03/206. Section V presents various approaches to evaluating risks arising from contingent liabilities, distinguishing between those explicit and implicit in nature. Appendix III contains crosscountry econometric evidence on the cost of banking crises.

> 13 See “Sustainability Assessments-Review of Application and Methodological Refinement”, IMF, 2003.

> 14 These shocks are based on the IMF (2003) and serve as a 95 confidence interval around the baseline. In particular, stochastic simulations show that the most extreme bound test provides an upper bound of the debt ratios that is likely to be exceeded only with a probability of less than 1 percent. The second most extreme bound test provides an upper bound likely to be exceeded with a probability between 1 to 5 percent.

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