**Table 3. Sensitivity of Burundi’s Debt to Small Changes in Macroeconomic Forecasts**

||**2013**|**2014**|**2015**|**2016**|**2017**|
|---|---|---|---|---|---|
|**Debt to GDP under the baseline**|33.7|33.9|34.1|34.5|**33.6**|
|**Impact of change in real GDP growth rate**||||||
|Lower GDP growth (-1%)|34.2|35.2|36.4|38.1|**38.8**|
|Highe GDP growth (+1%)|33.3|33.1|32.9|32.9|**31.8**|
|**Impact of change in Exchange rate depreciation**||||||
|Lower depreciation rate (-1%)|33.7|33.9|34.4|35.3|**35.2**|
|Higher depreciation rate (+1%)|33.8|33.9|34.1|34.5|**33.7**|

_Source_ : The author’s calculation.

**To address inherent uncertainties in macroeconomic projections, and more importantly, to take into account the structural vulnerabilities of Burundi’s economy to external shocks, below, we undertake a stochastic fiscal sustainability analysis.** We consider the impacts of external risks that the country is well-known to be exposed to, namely, volatilities in global coffee prices, rainfall, and aid flows. Each type of shock is defined as deviation from the central trend and is assumed to be normally distributed with a mean of zero and a standard deviation estimated by the variable’s historical data. Using Monte Carlo simulation, each shock is drawn randomly from its respective probability distribution, and is applied to the relevant endogenous variables to generate a set of alternative fiscal outcomes. The process is repeated 10,000 times to produce a probability distribution of possible fiscal outcomes. Fan charts are then used to illustrate the results.<sup>13,14</sup>

13 The analysis is a type of sensitivity analysis—the shocks are applied on a ceteris paribus basis, i.e., while one shock (e.g., to the coffee price) is being applied, other shocks (e.g., to rainfall) are not taking place. In addition, only the direct impact of the shock on the endogenous variables is considered, not indirect effects, including “feedback” and policy responses. For example, while applying shocks to coffee prices, the direct effect is on the values of exports, and thereby GDP and government revenues. No secondary effects or feedback are considered, such as possible adjustments in imports, interest rates, or exchange rates.

14 We do not estimate the combined effect of all three types of shocks. Usually such a combined effect is estimated simply by adding up the shocks (e.g., the DSA uses this approach). This is often misleading because (a) some shocks mitigate each other, (b) there will be secondary adjustments (e.g., interest rates, exchange rates), (c) there will be policy response by the government, and (d) there will be donor responses to shocks. This is why some studies estimate the impacts of combined shocks using the variance-covariance matrix estimated via VAR (Vector Auto Regression), which will summarize, in reduced form, the historical patterns of the combined responses from (a)–(d). For Burundi, we cannot implement this approach due to lack of long-term data. VAR usually takes a data series of 20 years or longer to be meaningful (many countries try to increase the sample by using the quarterly data). With WAR dummy running around 10 years (which causes structural breaks), Burundi's covariance matrix cannot be estimated robustly.

11