BS1780 Macroeconomics for Business
Problem Set 3
Assuming that the nominal interest rate, the inflation rate, the real GDP growth and primary deficit remain constant for the next year, we can compute the projected next year end debt as a percentage of GDP by using the equation:
In this case, dt is the public debt (as % of GDP) of 2011, which is 88%; i is the government interest rate 7% according to our assumption; π is the inflation rate, which was 2% if it is held constant constant in the next year; gr is -1%, the real GDP growth; and -st+1 is the primary deficit, which is 3%. Therefore:
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Since dt+1=1+i-g-πdt-st+1, the debt would keep growing if st+1 is negative. In the case of Cyprus, the real interest rate r equals to nominal interest rate 7% minus inflation rate 2%, so r=5%. Thus, Cyprus needs a primary surplus to sustain its debt when the interest rate remains at 7% as r>g. However, according to the case and our assumptions, Cyprus has a constant primary deficit. If we roll this forward one year to forecast the 2013 year end debt, we can see that it is 105%, a figure that greater than 100%. If we roll further to year 2015 as shown in Table 1, the ratio keeps going upwards, indicating that Cyprus would not be able to sustain its debt after 2013. Besides, as the ratio increases, the default risk for Cyprus increases, and as the default risk gets higher, panic will arise in domestic and international markets, which may result in economic downturn because of reasons like capital outflow. Even the country does not default, rating agencies like S&P and Fitch will lower the credit rating for the country when the debt-to-GDP ratio gets higher, which lead to creditors seeking a higher cost of debt for Cyprus to borrow and increase the country’s borrowing costs. Hence, Cyprus stopped borrowing and turned to IMF for lower interest rate when the interest rate goes above 7%.
Cyprus cannot borrow internationally, to finance its operating needs, it has to enter an agreement with IMF, in which a low-interest rate loan is offered to Cyprus, and in return, Cyprus need to meet the IMF conditions, which is reducing total deficit to 3% and primary deficit to 0%. In this case, we assume that Cyprus replaced all its debt with the loan from IMF, hence after the loan, its debt is comprised of IMF loan only. Therefore, the interest rate of its debt is the interest rate of IMF debt, 2.5%. Keeping all the other numbers unchanged, we have the debt ratio forecast table below.
Table 2: Debt ratio forecast – Change following IMF/Troika loan
| No loan
t | IMF loant | IMF loant+1 | IMF loant+2 |
Inputs | | | | |
Primary deficit (% of GDP) | 3 | 0 | 0 | 0 |
Interest rate (money market, %) | 7 | 2.5 | 2.5 | 2.5 |
Inflation (%) | 2 | 2 | 2 | 2 |
Real GDP growth (%) | -1 | -1 | -1 | -1 |
Public debt (% of GDP, end of t-1) | 88 | 88 | 89.32 | 90.66 |
| | | | |
Miscellaneous calculations | | | | |
Real interest rate (%) | 5.00 | 0.50 | 0.50 | 0.50 |
| | | | |
Components of change in B/Y | | | | |
(A) Real interest | 4.40 | 0.44 | 0.45 | 0.45 |
(B) Growth | 0.88 | 0.88 | 0.89 | 0.91 |
(C) Primary deficit | 3.00 | 0.00 | 0.00 | 0.00 |
Total | 8.28 | 1.32 | 1.34 | 1.36 |
| | | | |
Year end debt (% of GDP) | 96.28 | 89.32 | 90.66 | 92.02 |
Looking at the debt ratios, it can be seen that debt ratios decreased considerably after the loan, from 96.28% to 89.32%, indicating an alleviated debt pressure for Cyprus. Most of this change is due to the decrease in primary deficit and interest...