#### Analyzing Debts and Deficits

Analyzing Debts and Deficits:

The first question to inquire about a government that is running a persistent deficit is- Can it go on? Is it possible for the government to carry on running its current deficit indefinitely or else must policy change--possibly for the better however as well quite possibly for the worse?

The variable to look at to charge whether the government's current fiscal policy is sustainable is the time path of the ratio of the government’s total debt to GDP the debt-to-GDP ratio D/Y. A fiscal policy can be sustainable if the debt-to-GDP ratio is heading for a steady state.

We are able to analyze the debt-to-GDP ratio D/Y by looking to see if it heads for some steady-state value. At a stable state value both the numerator D and the denominator Y will be growing at the similar proportional rate. We recognize that real GDP grows in the long run at a proportional annual rate n + g where n is the annual rate of growth of the labor-force as well as g is the annual rate of growth of the efficiency of labor.

Define the proportional growth rate of the debt D? Adding time subscripts to remain things clear the debt next year will be equal to:

Dt+1 = (1-π)Dt + d

The real value of the debt get smaller by a proportional amount π as inflation erodes away the real value of the debt principal owed by the government and grows by an amount equal to the officially-reported cash deficit d. As the economy raise tax revenues grow roughly in proportion to real GDP and spending grows in proportion to real GDP too. Thus it makes sense to focus not on the deficit itself but on the deficit as a share of GDP call it little delta δ:

δ = d/Y

Subsequently the proportional growth rate of the debt is:

The debt-to-GDP ratio will be steady when these two proportional growth rates of GDP and of the debt are equal to each other

n + g = -π + δ x (Y/D)

This happens when:

D/Y = δ/(n + g + π)

This is the steady-state level in the direction of which the debt-to-GDP ratio will head. This is the level reliable with a constant cash-balance deficit of ? percent of GDP in an economy with long run inflation rate π as well as with long run real GDP growth rate n+g.

Why then do economists converse about deficit levels as being unsustainable? For every deficit as a share of GDP δ the debt-to-GDP ratio heads for its well-defined steady-state value δ/(n+g+π).

This nevertheless is only half the story. The proportion of the debt that the government needs to issue to GDP heads for a stable value yes. However are there enough investors in the world willing to hold that amount of debt? The superior the debt-to-GDP ratio the more risky and investment do financier judge the debt of a country. The less keen they will be to buy and hold that debt.

A higher debt-to-GDP ratio creates investments in the debt issued by a government more risky for two reasons. First revolutions or other additional peaceful changes of government happen. One of the things a new government should decide is whether it is going to honor the debt issued by previous governments. Are these debts the obligations of the nation which as an honorable entity honors its commitments? Or are these debts the irresponsible mistakes made by and obligations of a gang of thugs unrepresentative of the nation to whom investors must have known better than to lend money for the thugs to steal? The holders of a government’s debt uneasily await every new government’s decision on this issue.

The elevated the debt-to-GDP ratio the greater the temptation for a new government to repudiate debt issued by its predecessor. Therefore the riskier is buying and holding a portion of a country’s national debt.

Subsequent even if there is no change in government it is still the case that a government is able to control the real size of the debt it owes through controlling the rate of inflation. The nominal interest rate to be compensated on government debt is fixed by the terms of the bond issued. The real interest rate paid on the debt is equivalent to the nominal interest rate minus the rate of inflation and the government controls the rate of inflation.

Therefore a government that seeks to redistribute wealth away from its bondholders to its taxpayers is able to do so by increasing the rate of inflation. Te additional inflation the less is the government’s debt worth as well as the lower is the real taxes that have to be imposed to pay off the interest as well as principal on the debt. Whether a government is probable to increase the rate of inflation depends on the costs and benefits and raise the rate of inflation does have important political costs. Nevertheless the higher the debt-to-GDP ratio the greater the benefits to taxpayers of a sudden burst of inflation. When the debt-to-GDP ratio is equivalent to 2 a sudden 10% rise in the price level reduces the real wealth of the government’s creditors as well as increases the real wealth of taxpayers by an amount equal to 20% of a year’s GDP. By contrast when the debt-to-GDP ratio is equivalent to 0.2 the similar rise in the price level redistributes wealth equivalent to only 2% of a year’s GDP.

Therefore the government’s potential creditors should calculate that the greater the debt-to-GDP ratios the greater are the benefits to the government of inflation as a way of writing down the value of its debt. The higher the debt-to-GDP ratio the more probable is the government to resort to inflation. Therefore the higher the debt-to-GDP ratio, the more risky are investments in a government's debt.

A deficit is sustainable merely if the associated steady-state debt-to-GDP ratio is low enough that investors judge the debt safe enough to be willing to hold it. Think of every government as having a debt capacity a maximum debt-to-GDP ratio at which investors are enthusiastic to hold the debt issued at reasonable interest rates. If this debt capacity is go beyond then the interest rates that the government must pay on its debt spike upwards. The government is countered with a much larger deficit than planned (as a result of higher interest costs). Either the government should raise taxes or it must resort to high inflation or hyperinflation to write the real value of the debt down.

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