<mark>recall Note 4 above). But overall, the composite real interest rate</mark> _<mark>lowered</mark>_ <mark>d by 6.5 percentage points of d, suggesting a highly negative real interest rate on local currency debt that outweighed a highly positive real interest rate (inclusive of the capital loss from currency depreciation) on $ debt. These effects need to be quantified by breaking r down into its local currency and $ components. To do this, we would need to have the share of $ debt at the end of 2021, the depreciation of the Sri Lankan</mark> cc <mark>rupee (LKR) against the $ based on end-year exchange rates and the “effective interest rate” broken down into its LKR and $ components. Such information would capture the vulnerability of the government’s balance sheet to currency collapses on account of $-denominated debt, a vulnerability AEs are typically not subject to. The formulas for the composite nominal ( i ) and real ( r ) interest rates and the breakdown of the composite real interest rate into its local currency (L) and foreign currency ($) components are given</mark> cc cc <mark>below, drawing on equation (6) above and related commentary: (9) i</mark> , where is the local currency equivalent of the interest rate on $-denominated debt, , translated into<sup>cc</sup> = (1 −αα)ii<sup>LL</sup> + αα[ii<sup>$</sup> (1 + αα) + αα] = (1 −αα)ii<sup>LL</sup> + ααii<sup>$,LL</sup> local currency terms using the formula in square brackets on the RHS of (9).<sup>6</sup> And: ii<sup>$,LL</sup> ii<sup>$</sup> (10) = −1 = <u>� � ( )</u> , 1+ii<sup>cc</sup> ii<sup>cc</sup> −ππ<sup>LL</sup> ii<sup>LL</sup> −ππ<sup>LL</sup> ii<sup>$,LL</sup> −ππ<sup>LL</sup> where rr<sup>cc</sup> and 1+ππ<sup>LL</sup> are the real interest on local currency debt and on $-denominated debt translated fully 1+ππ<sup>LL</sup> = (1 −αα) 1+ππ<sup>LL</sup> + αα 1+ππ<sup>LL</sup> = (1 −αα)rr<sup>LL</sup> + ααrr<sup>$,LL</sup> into local currency terms and including the capital loss on $-denominated debt as the result of currency depreciation. Pulling things together, we can write: rr<sup>LL</sup> rr<sup>$,LL</sup> (11) − −1 = + ~~[~~ rr1cc−g ~~]~~ −1<sup>,</sup> and by comparison with equation (6), ddtt ddtt ppddtt +gg ddtt <mark>r = r +</mark> α , which can be directly verified using the information 1+ <mark>in equations (3), (9) and (10).</mark> cc ππLL **_NB:_** and are notional interest rates calculated, respectively, by dividing interest payments on local currency debt for year t by the local currency debt stock at the end of (t-1) and on $-denominated debt assumed to be paid in local currency at the end of year t divided by the $ debt stock expressed in ii<sup>LL</sup> ii<sup>$</sup> (1 + αα) local currency at the end of the previous year, (t-1).<sup>7</sup> <mark>A final note to conclude this section: the residuals both for Japan (-5.6% of GDP in 2021) and Sri Lanka (+5.9% of GDP in 2022) are significant and it would be worthwhile to provide some explanation.</mark>

# **<mark>IV. Suggestions for Improvement of the 2023 MAC DSA Template</mark>**

<mark>The 2023 IMF MAC DSA template could be usefully modified to account for the special needs of EMs relative to AEs.</mark>

- <mark>First, it would be useful to compute the composite real interest rate to mimic a single-currency environment to get an idea of the sustainability of the trajectory of d based on pd and r-g.</mark>

> 6 Suppose the initial exchange rate is 1 and $100 is borrowed for one year at 4% ( ) and the currency depreciates by 10% (ε=0.1) to 1.1 a year later when the interest and principal are due. Then the interest payment of $4 becomes 4.4 in local currency terms while the principal is now 110, implying a total effective interest rate in local currency terms of ii<sup>$</sup> 14.4/100 = 0.144=0.04X1.1 + 0.1, or 14.4%. This is essentially the expression in square brackets on the RHS of (9) and is denoted . See Box 1 in Gill and Pinto (2023) for a complete explanation. 7 Once again, please see Box 1 in Gill and Pinto (2023). ii<sup>$.LL</sup>

11