J Brauer | © Stone Garden Economics
To help readers better understand the turmoil on the European financial markets, The Economist, a respected weekly news magazine, published a brief [here] on the important elements that play into government budget deficits and accumulated debt. I thought it worthwhile to reexplain this more elaborately and also to provide a numerical, albeit hypothetical, example.
Apart from the amount (or stock) of debt itself, five crucial variables need to be considered. Let’s list them, and also let’s give them an abbreviation, a letter, by which to refer to them. First is the nominal interest rate—refer to it with the letter i—due on government debt. Second comes the rate of price inflation, p. The third is the difference between the first two. Called the real interest rate, we use r as the relevant letter. (Thus, i – p = r, and I’ll explain in a moment just what this means.) Fourth is the primary government budget balance. Equivalent to your household budget without the mortgage payment, this is what the government’s budget would be when interest is subtracted out. Refer to this with the letter b. And fifth is the economic growth rate of the country, or g. The debt itself is called d.
So we have d, i, p, r, b, and g. Got it?
Now suppose that in 2010 economic output or GDP was $100,000, government debt (d) was $50,000, and the nominal interest rate (i) was 5%. Thus, the ratio of debt-to-GDP is 50%. The interest due on the debt is $2,500, and this will have to be part of the government’s budgeted outlays. Next, assume that tax receipts were $8,000 and that total outlays were $10,500. Thus, the government budget deficit is $8,000–$10,500 = –$2,500, and government will have to borrow the “missing” $2,500 from Peter to pay $2,500 of interest to Paul. Still, it can be argued that the government budget itself is in balance because the tax receipts cover all of the actual functions of government, except for those pesky interest payments. And so we say that the “primary” budget is in balance, b = $0.
Next, assume that price inflation, p, is 3% and also that I loan the government $2,500 for one year at 5% nominal interest (i). At the end of the year, I get $2,625 ($2,500 principal, plus $125 in nominal interest). But because of inflation, what I can buy with those $2,625 is 3% less than at the beginning of the year. In terms of purchasing power, the real value of what government pays me back is only $2,575. True, I do make $75, but the other $50 is “eaten up” by inflation.
We learn that it is in government’s interest to drive up the inflation rate (p)! Conversely, it is in lenders’ interest to ask for a higher nominal interest rate (i) so as to keep the real interest rate (r) high as well. What matters is r, the real interest rate. If government manages to drive up the inflation rate, p, in order to reduce the real interest rate (r) then it can lower its interest burden in favor of taxpayers but at the expense of lenders. Politicians, and conniving (or ignorant) voters, neatly set up one group against the other. But lenders are smart and quick, and they can refuse to lend, driving governments to the wall. And that is part of what’s happened in the euro zone.
In what follows I assume, for convenience, an unchanged real interest rate of r = 2%. Thus, the results are not driven by a fight over inflation-adjusted returns to lenders but by additional considerations.
Let’s recap. Thus far we have brought the following variables into play: d, i, p, r, and b. The only one missing is g, the economy’s growth rate. This is important because higher growth usually means higher tax receipts and lower government outlays (think, fewer unemployment expenses). Therefore a higher g usually means an improved budget balance. In our example, suppose the economy grows at 2%, that tax receipts also grow by 2%, and that outlays fall by 2%. (All in inflation-adjusted, or real, terms.)
Under these generous assumptions, a spreadsheet simulation (keeping r at 2%) shows that overall debt will continue to rise until the year 2014, even as the debt-to-GDP ratio already falls below the 50% mark in 2012.
The reality governments face today, however, is far from this rosy. We can simulate this by changing a single number: Suppose that, to start off with, government’s primary outlays (without interest payments) are $10,000 instead of $8,000, and then fall by 2% each year as the economy grows. What happens in the spreadsheet simulation? Despite the still rather rosy scenario, the total amount of debt rises each year until 2020, and the debt-to-GDP ratio does not fall below 50% until the year 2023!
Now change a second assumption, namely that government primary outlays always fall when the economy grows. In our simulation, with 2% growth, let’s say we keep government primary outlays at a constant $10,000: no fall, no rise. What happens? Debt accumulation rises until the year 2030, and the debt-to-GDP drops below 50% only in 2035.
Finally, add in a third change in assumptions. Suppose growth is only 1% (still keeping r = 2%; outlays = $10,000). What happens? Debt rises continuously until the year 2058, and the debt-to-GDP ratio dips below 50% by saintly 2082. I say “saintly” because by that time I’ll be a saintly 125 years old and very much will need to rely on social security payments and Medicare. Put differently, primary outlays are not going to stay at $10,000—making the simulation results even worse.
The real-world is more complex, requiring more sophisticated math. But the point here is pedagogical and you get the main ideas: (1) the budget situation is desperate; (2) we need growth; and (3) budget deficits urgently need to be brought under control. To read about one proposal a colleague and I made, click [here] and [here] and [here]. It goes back six years, and nobody listens. But, then, economists are used to that.
J Brauer is Professor of Economics, James M. Hull College of Business, Augusta State University, Augusta, Georgia, USA.
