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# By the end of the 1970s , the federal debt -to-GDP ratio was 27 percent (in the notation of the text, b = 0. The progr am spending ratio did not...

By the end of the 1970s, the federal debt-to-GDP ratio was 27 percent (in the notation of the text, b = 0.27). The program spending ratio did not exceed the tax-to-GDP ratio by much: (g - t) averaged about 0.007 during the 1975-1979 period. Fourteen years later, by 1993, the debt ratio had risen to 73 percent--an increase of 46 percentage points. The controversy has concerned how much of this increase should we attribute to each of two causes: systematic overspending by the government versus world developments and contractionary Canadian monetary policy--both of which caused lower real growth rates and higher real interest rates during this 14-year period. These developments meant that the government lost revenue at the very time that it had higher employment-insurance obligations. Thus, even though (g - t) rose over the 14-year period, many have argued that a significant part of that increase should not be interpreted as "overspending' by the government.

According to this view, (g - t) had to rise because of developments that were beyond the control of fiscal policy.

As a basis for comparison, let us assume that those external events did not happen. Also, let us assume that there was no independent increase in (g - t) either. Finally, let's assume that the gap between the interest rate and the growth rate was only 2.6 percentage points--1.5 percentage points below the gap that actually occurred over the 1980-1993 period. These assumptions give us some idea about what the debt buildup would have looked like if neither of the alleged causes pertained.

1. Use a spreadsheet to conduct this simulation. As explained in the text, the relationship involved is,

(next year's b) = (g - t) + (r - n)(this year's b).

Start off with this year's b equal to 0.27; and assume that (r - n) and (g - t) remain constant at 0.026 and 0.007, respectively. What values does b reach after 14 years?

2. Now let us add the bad news events that were beyond the control of the government. Let's assume that these events (the downturn in productivity growth and the contractionary monetary policy) had two effects: they widened the (r-n) gap by 1.5 percentage points and forced the government to double its (g-t) gap. To simulate this second scenario, use the same equation and the same starting value for b (0.27). But this time, set (r-n) and (g-t) to 0.041 and 0.014, respectively. What value does b reach after 14 periods this time?