<mark>surpluses and bring r down; in the short-run, such fiscal consolidation is likely to hurt g, but the improved macroeconomic climate will give private sector investment and growth a boost over the medium run. (We rule out default and inflating away local currency debt.)</mark> <mark>Most EM and LIC DSF country governments borrow both in local currency, typically at market terms, and in foreign exchange, say, the US dollar ($) at concessional and market terms. In order to apply the framework embodied in equation (a) above, one would need to mimic a single-currency environment. The challenge is presented by $ borrowing, as illustrated with a numerical example:</mark>

||Time 0|Time 1|
|---|---|---|
||$100|$104|
|1. Exchange rate(local currency per$)|1.0|1.1|
|2. Local currency-equivalent debt|100|114.4|
|3. Interestpayment in$||4.0|
|4. Interestpayment in local currency<br>||4.4<br>|

4. Interest pay <u>y</u> 4.4 <mark>The government borrows $100 at time 0 at i =4% per period. The exchange rate (local currency price of $) at time 0 is 1.0 but depreciates to 1.1 by time 1. As a result, the interest due of $4 becomes 4.4 in local currency terms, shown in lines 3 and 4 of the table. This 4.4 will show up in the</mark><sup>$</sup> _<mark>fiscal balance</mark>_ <mark>. But the impact on the government’s</mark> _<mark>balance sheet</mark>_ <mark>is much bigger, as shown in line 2 at Time 1. The effective interest rate is 14.4%, of which 4.4 will show up in the fiscal accounts and the remaining 10 on the balance sheet and in the headline debt number. In other words, the true local currency equivalent interest rate of $ borrowing is 14.4%. Formally, if x denotes the</mark> end-year exchange rate expressed as local currency per $ and ~~,~~ its growth rate or the rate of <mark>depreciation, then the local currency equivalent of i =4% is given by</mark> xx�= xxttxx−xxtt−1 <mark>i</mark> tt−1 <mark>(1 + x�) + x� = 0.04 X1.1+0.1=0.044 +</mark> 0.10=0.144=14.4%. This is simply _ex post_ interest rate parity.<sup>$$</sup> <mark>Now suppose the government had also borrowed 200 in local currency at time 0 at 7%. Then its accounts would show interest payments of (4.4+14)=18.4 in local currency units. The LIC DSF calculates the effective interest rate i as interest payments divided by the local currency-equivalent debt stock at the end of the previous period, giving i=18.4/300 = 6.13%, which can be converted into real terms using the GDP deflator. This interest rate of 6.13 = (2/3)x7 + (1/3)X4.4, where 2/3 and 1/3 are the respective weights of local currency and dollar debt at the end of</mark> the previous period.

<mark>What about the balance of 10, the capital loss on $ debt? This goes into the exchange rate contribution to the change in the headline debt number in the LIC DSF template, and is given by (currency depreciation x share of $ debt in total debt at the end of the previous period x total debt at the end of the previous period) =</mark> 0.1X(1/3)x300=10.

<mark>However, to mimic a single-currency environment for assessing debt sustainability based on (r-g), this capital loss needs to be merged with the interest payment of 18.4 to give a composite nominal interest rate of (18.4+10)/300 = 9.47%. This can in turn be written as a weighted average of the interest rates on local currency and $ debt as 9.47 = (2/3)x7 + (1/3)x14.4, and the real equivalents can be obtained by deflating 9.47, 7 and 14.4 by the GDP deflator. For example, if inflation measured by the GDP deflator were 6%, then the composite real interest rate r = (1.0947/1.06) – 1 = 3.27%. This r captures the impact of currency depreciation on the $ component of debt and is the r that should be used for (r-g). It is useful to break it down into its local currency and $ components, 0.94% and</mark> 7.92% respectively, to gauge what is driving r, in this case $ debt, clearly.

<mark>There are two advantages to merging the capital loss on foreign currency debt with its interest cost. First, it gives a more accurate picture of the cost of $ borrowing. For example, if the government were to simply compare 7% on local currency debt with 4.4% on $ debt, it might wrongly conclude that dollars are cheaper to borrow. Based on the second author’s conversations with investment banks in Ghana in early 2017, this was the argument they used to persuade the Government to issue $-denominated debt in the domestic market. Second, it enables a clear picture of debt dynamics by amalgamating currency depreciation with the interest rate, making it comparable to r in a single-currency environment. In contrast, there is little insight to be gained analytically or for borrowing</mark> <u><mark>purposes by treating currency depreciation as a separate effect.</mark></u> 10