Deficit: can be seen as a return?

Question

Suppose I have a series of debt as % of GDP.

By computing returns on this serie e.g.

debt as % of GDP in year 1 is 50% in year 2 is 60%

I compute $(60\%-50\%)/50\%$ can I interpret this measure as a sort of deficit for year 1-2? Hence, deficit for this period is 20%. Or shall it rather be the difference $10\%$?

Answer 1

None of these. Your measure is very different from the deficit. But, more generally, if this is all you know, you can't calculate it. You would also have to know GDP or the debt. Here is an example to show that it does not work:

+------+------+---------+------+-------------+--------------+
| YEAR |  GDP | Deficit | Debt | Debt to GDP | Your Measure |
+------+------+---------+------+-------------+--------------+
| 2011 |  100 |      10 |   10 | 10%         |              |
| 2012 |  110 |      12 |   22 | 20%         |            1 |
| 2013 |  120 |      14 |   36 | 30%         |          0.5 |
+------+------+---------+------+-------------+--------------+

Answer 2

What you trying to say is similar to this

X earn $10,000 , bank loan of $5,000,  thus debt to earning = 50% 
Y earn $100,000 , bank loan of $50,000, thus debt to earning = 50% 
because the debt to earning ratio is both 50%, so X = Y . 

THIS IS INCORRECT. Even the debt ratio is same as 50%, you CANNOT make a direct equation.

You cannot make it right by playing with this kind of ratio, e.g.

Year 1 , GDP 1000 , deficit 500, debt to GDP ratio = 50% 
Year 2 , GDP 2000 , deficit 1200, debt to GDP ratio = 60%

Both base value are different, so you cannot put them inside any equation.

Nevertheless, this is a common problem of people who practice economy attempt to apply mathematics rules.