macro notes: fiscal deficits - american universityoutlays and receipts debt dynamics graphical...

Outlays and Receipts Debt Dynamics Graphical Analysis Algebraic Analysis Sustainability Budget Crisis Ricardian Equivalence Debt and Interest Rates Stabilizing Fiscal Responses Bibliography

Macro Notes: Fiscal Deficits

Alan G. Isaac

American University

2009


“Any government, like any family, can for a year spenda little more than it earns. But you and I know thata continuation of that habit means the poorhouse.”– FDR, radio speech July 30, 1932


“How did you go bankrupt?” Bill asked.“Two ways,” Mike said. “Gradually and then sud-denly.”– Hemingway (in: The Sun Also Rises)


This presentation draws on Farmer (2002, ch.14) and Jones(2011, ch.17).


There are 1011 stars in the galaxy. That used to bea huge number. But it’s only a hundred billion. It’sless than the national deficit! We used to call themastronomical numbers. Now we should call them eco-nomical numbers.Attributed to Richard P. Feynman, as quoted by Jones(2009, p.386)


Just how big is government?Let us start by looking just at the federal government:


Total Outlays 2009 3517.7

National defense 661.0

International affairs 37.5

Health 334.3

Medicare 430.1

Income security 533.2

Social security 683.0

Net interest 186.9

Other 651.6

Total Receipts 2105.0

Individual income taxes 915.3

Corporation income taxes 138.2

Social insurance and retirement receipts 890.9

Other 160.5

Surplus -1412.7


Lesson 1: Governments can spend more than their receipts.These number seem big. Are they?One way to assess the size of government is to look at outlaysand revenues as a fraction of GDP.Continue to look just at the federal government:


US Federal Outlays and Receipts

Source: Jones (2009)


US Federal Outlays and Receipts

Data Source: FRED


The Federal budget is out of control, and we facerunaway deficits of almost $80 billion . . .– Ronald Reagan, 1981http://www.reagan.utexas.edu/archives/speeches/1981/20581c.htm

Reagan proved deficits don’t matter.– Dick Cheney, 2002, in response to Treasury Secre-tary Paul O’Neill’s concerns.

Was this an economic claim, or a political claim?


US Federal Budget Balance

Data Source: FRED


US Federal Budget Balance (% GDP)

Data Source: FRED


These number also seem big. Are they?One way to assess this is to make comparsions with the rest ofthe world.


Government Expenditure: Cross Country Variation

Source: Jones (2008)Note: Euro = France, Germany, Spain, and Italy


Define the primary deficit:

Dpt = Gt − (Tx− Tr) (1)

The total deficit is the primary deficit plus the interestpayments on government debt.

Dtotalt = Dp

t + iBt (2)

Here B is the nominal supply of short term bonds, i is theshort term nominal interest rate, and Dp is the nominalprimary deficit.


The annual evolution of nominal government debt:

Bt+1 ≡ Bt + itBt + Dpt︸︷︷︸

total deficit

(3)

We assume that bonds are very short maturity just to keepthings simple: that way there is no change in value ofgovernment debt when the interest rate changes. (Anotherway we will keep things simple is by ignoring tax collections onthe interest on government debt, which would show up in Dp.)


Federal Debt and Deficits (U.S.)

The important point here is that the deficit drives the debt:

Source: Jones (2008)Note: measure is debt held outside of government.


In 2005 the debt-to-GDP ratio was about 0.37, which is about$15,000 per person.About half was owed to U.S. residents, and half to foreignresidents. (We cannot say that we owe it to ourselves.)In 2010 the debt to GDP ratio exceeded 90%, or about$45,000 per person.


Debt-GDP Ratios

The U.S. federal debt to GDP ratio seems large; how does itcompare to other nations? Until recently:

Source: Jones (2011)Note: measure is debt held outside of government.


Debt-GDP Ratios

The following graph makes things look worse, but it uses grosspublic debt. (E.g., it includes Fed and intragovernmentalholdings of Treasury issue.)

Source: http://www.usgovernmentspending.com/federal_debt_chart.html

http://www.usgovernmentspending.com/federal_debt_chart.html


Debt-GDP Ratios: Gross and Net

Source: http://www.usgovernmentspending.com/federal_debt_chart.html

http://www.usgovernmentspending.com/federal_debt_chart.html


OECD: Net Debt to GDP

Source: ERP (2010, fig 5.6)


Budget considerations are inherently dynamic.

Static analysis: examine the economy at a point in time.

Dynamic analysis: examine how the economy changes with thepassage of time.

The linkages between stocks and flows are a naturalapplication of dynamic analysis. E.g., the stock of governmentdebt changes as a result of the deficit (a flow variable).


We begin with a flow version of the government budgetconstraint:

Gt + Tr + iBt︸︷︷︸Uses

= Txt + ∆Bt + ∆Mt︸︷︷︸Sources

(4)

We can say the uses of funds equals the sources of funds. Forsimplicity, we will ignore seigniorage revenue for now. (That is,set ∆M = 0.)


The primary deficit is the reported deficit less the governmentsnet interest payments. The total deficit is therefore itBt + Dp

t .Combining terms in Bt−1 and assuming a constant interestrate we can rewrite this as

Bt+1 = (1 + i)Bt + Dpt (5)

To keep things simple we have assume that bonds have amaturity of one period.1 Also for simplicity, we assume thatthe interest rate is a constant. The result is an equation thatlinks the evolution of the bond supply to its past value: adifference equation.

1The maturity of a bond is the period from the date of issue to thedate of redemption (when the principal must be repaid).


Difference equations: the past of a state variable determinesits future values. Difference equations allow us to representdynamics.


Recall Dp is the primary deficit: the difference betweennon-interest government outlays and government revenues(Tx).Non-interest government outlays include governmentexpenditures G plus non-interest transfer payments.The primary deficit differs from the reported deficit by theamount of the interest payments on government debt.


Reported vs. Primary Deficit for Postwar US

DeficitYear Receipts Outlays Interest Reported Primary

1945 45.2 92.7 3.1 47.5 44.41992 1091.3 1381.6 199.6 290.3 90.72001 1991.1 1862.9 206.2 -128.2 -334.42002 1853.1 2010.9 170.9 157.8 -13.12003 1782.3 2159.9 153.1 377.6 224.52004 1880.1 2292.9 160.2 412.8 252.62005 2153.6 2472.0 184.0 318.4 134.42006 2406.9 2655.1 226.6 248.2 21.62007 2568.0 2728.7 237.1 160.7 -76.42008 2524.0 2982.6 252.8 458.6 205.82009 2105.0 3517.7 186.9 1412.7 1225.82010 2165.1 3720.7 187.8 1555.6 1367.82011 2567.2 3833.9 250.7 1266.7 1016.0

Source: Outlays and Receipts in billions of dollars are from the ERP 2006 Table B-78. Interest payments are fromthe ERP Table B-80.


We see US economic history embodies a variety of experienceswith deficits. In levels, the postwar period saw budgets thatlook balanced compared to recent history. We can see thedeficit explosion in the 1980s and the correspondingacceleartion in debt accumulation. In this context the risingpolicy concern about federal deficits in the late 1980s andearly 1990s is easy to understand. However data in levels failsto control for the size of the economy.


If we look at the debt and deficit as a proportion of GDP,things still look bad but they do not look quite so shocking.While the deficits of the 1980s and early 1990s are unusualpeace time events both in their size and their presistence, as aproportion of GDP we saw much larger debt and deficits in thewake of WWII. Still, there is an important difference. Whenthe government produces a benefit for future generations, aswhen it fights WWII, it may seem reasonable to impose costs(here, taxes to repay the debt) on those future generations.The deficits of the 1980s and those of the 2000s do not seemto have been run to purchase corresponding benefits.


It is more informative to deflate debts and deficits by GDP.Governments tax GDP to pay off the debt, so the debt-to-GDPratio gives a better sense of our ability to pay off our debt.


Recall our basic debt accumulation equation:

Bt+1 = Dpt + (1 + i)Bt (6)

This equation embodies our basic debt dynamics: theaccumulation of debt over time. This said that debt grows dueto the primary deficit and due to interest rate payments onoutstanding debt.We can also write this as

Bt+1 − Bt

Bt=

Dpt + iBt

Bt=

D rt

Bt(7)

The deficit to debt ratio is the growth rate of of debt. (So thedebt to GDP ratio will stabilize when the deficit to debt ratioequals the growth rate of GDP.)


We now rewrite this as a fraction of GDP:

Bt+1

Y Nt

=Dp

t

Y Nt

+ (1 + i)Bt

Y Nt

(8)

Recall that Y Nt = (1 + Y N)Yt−1, so we can rewrite our budget

dynamics asBt+1

Y Nt

=Dp

t

Y Nt

+1 + i

1 + Y N

Bt

Y Nt−1

(9)

Let bt = Bt/YNt−1 and let the primary deficit to GDP ratio be

constant:

bt+1 = d +1 + i

1 + Y Nbt (10)


This version of our debt dynamics equation also says that debtgrows due to the primary deficit and due to interest ratepayments on outstanding debt, but since we are looking at thedebt-to-gdp ratio one additional factor enters: the rate ofgrowth of GDP. Since we are focusing now on thedebt-to-GDP ratio, when GDP grows this ratio shrinks and weneed to account for that.


At this point is is very useful to think about a special case:d = 0. In this case we see that the debt-to-GDP ratio grows ifi > Y N but shrinks if i < Y N . That is, borrowing to make ourinterest payments adds to the debt, but this can be offset byGDP growth. On this observation hinges the entire question ofwhether budget policy is sustainable. If the debt-to-GDP ratiogrows unbounded, eventually the interest payments on thedebt will exceed the entire GDP. At this point (and obviouslyfar before this) a government can be considered bankrupt: itstax base can no longer provide the revenues to meet itscurrent interest obligations.2

2At this point we do not address the possibility of “Ponzi scheme”financing, where addtional borrowing would be undertaken to make theinterest payments.


Alternative (ERP 2010, p.148) Analysis

Write the flow constraint Bt+1 = Dpt + (1 + i)Bt as

(1 + Y )Bt+1

Y Nt+1

=Dp

t + iBt

Y Nt

+Bt

Y Nt

(11)

(since Y Nt+1 = (1 + Y )Y N

t ) or

(1 + Y N)bt+1 = d rt + bt (12)

Set the reported deficit to GDP ratio constant and solve forbss :

(1 + Y N)bss = d r + bss (13)

so that

bss =d r

Y N(14)


Alternative (ERP 2010, p.148) Analysis

Intuition: if the debt to GDP ratio is constant, then debt isgrowing at the same rate as GDP, and the growth rate of debtis the deficit to debt ratio. I.e., Y N = d r/b in the steady state.

Growth (Y N) Policy (d r ) Implied Debt (bss)

5% 1% 20%4% 4% 100%


The solution to a difference equation tells us the value of thestate variable (in this case, the debt-to-gdp ratio) at eachpoint in time. We can illustrate the evolution of thedebt-to-gdp ratio graphically.


In figure 41 we show how a graph can be used to analyze debtdynamics. Note that both axes measure debt, but at differentpoints in time. The horizontal axis is labeled bt and thevertical axis is bt+1.The graph includes a 45 deg line, along which bt+1 = bt . Thatis, along this line the debt-to-GDP ratio is not changing. Wewill refer to this as the steady-state locus.The graph also includes another line, which represents ourdebt dynamics. For any current level of debt bt , the height ofthe line is the debt next period. So given an initial level b0 ofthe debt-to-GDP ratio, we can follow the evolution over timein this economy.We call the list of values taken over time the solution of thedifference equation 10. Note that in the case we have drawnhere, the debt-to-GDP ratio gradually approaches the steadystate locus.


Stable Debt Dynamics

b(t-1)

b(t)

b(0) b(1) b(2)


Recall that our debt dynamics were laid out in equation (10),which we repeat here for convenience.

bt = d +1 + i

1 + Y Nbt−1

Again we simplify by holding constant the primarydeficit-to-GDP ratio, the interest rate, and the growth rate ofGDP. So

bt = d + ρbt−1 (15)

Where ρ = (1 + i)/(1 + Y N).


In the steady state, the debt-to-GDP ratio is not changing. Ifthe economy is at the steady state, it stays there.

b = d + ρb (16)

Solving for the steady-state value of b we get

b =d

1− ρ=

1 + Y N

Y N − id (17)

Note for example that if Y N − i < 0 but d > 0, the steadystate level of debt is negative.


We now ask if the steady state is stable. That is, if we arenear the steady state, will me move toward it? Let usapproach that question by subtracting the steady state valueof b from both sides of equation 15 to get

(bt −d

1− ρ) = ρ(bt−1 −

d

1− ρ) (18)

We see the distance of b from its steady state will be shrinkingiff |ρ| < 1. Since interest rates and GDP growth rates arepositive, we are interested in whether ρ < 1. Equivalently, fora stable steady state we need i < Y N .


Unstable Debt Dynamics

b(t-1)

b(t)

b(0) b(1) b(2)


If we compare the three-month Treasury bill rate with thegrowth rate of nominal GDP for the US, we find another wayin which the 1980s were exceptional. From 1940 until 1979,we find i < Y N , suggesting stable debt dynamics. The interestrate spike of the early 1980s reversed this inequality,suggesting that debt dynamics had become unstable. Finally inthe mid-1990s we seemed once again to have restored i < Y N .


1980 was a turning point for the OECD as a whole, not justfor the US. After 1980, we find i > Y N . Did US fiscal ormonetary influence impose this on the world?


These changes in the US have been associated (e.g., byFarmer (2002,p.320)) with two policy events: the replacementof Arthur Burns by Paul Voker as chairman of the Fed inAugust 1979 (which led to a radical revision of monetarypolicy that October), and the Omnibus Budget ReconciliationAct of 1993. The first event clearly led to a surge in interestrates. The uniqueness of the second event is morequestionable however, since the 1980s and 1990s saw repeatedlegislative attempts to deal with surging budget deficits.


Major Statutes:1984 PL 98-369 Deficit Reduction Act ($51B tax increase,$58B less defense)1985 PL 99-177 Gramm-Rudman-Hollings Anti-Deficit Act(provided for automatic cuts but only reduced deficit by $12Bin 1986)1987 PL 100-202, 203 Omnibus Reconciliation Act (variousoutlay reductions)1990 PL 101-508 Omnibus Reconciliation Act (tax hike forhigh income households)1993 PL 103-66 Omnibus Budget Reconciliation Act(increased taxes and lower spending)1997 PL 105-33 Omnibus Reconciliation Act (cuts in Medicareand disretionary spending)


Despite all this legislation, it was not until 1993 that thebudget situation clearly moved toward long term improvement.Part of the improvement was of course due to the stronggrowth during the Clinton administration, which improvedfederal revenues.


Let us break this experience into periods. Postwar:1946–1980. Reagan-Bush: 1981–1992. Clinton: 1993–2000.In each can we can calculate an average value for d , Y N , andi . Table ?? reports the results of Farmer (2002).3

3In the last line of this table, I have corrected Farmer’s value for theClinton era as reported in his Figure 14.8, which (based on his data)misplaced the decimal point. These results are illustrated by Farmerfigures 14.6, 14.7, and 14.8.


Stability by Period: Farmer’s Results

Postwar Reagan-Bush Clintond -1.2% 0.7% -1.9%

Y N 7.5% 6.89% 5.5%i 4.1% 7.5% 4.9%

(1 + i)/(1 + Y N) 0.97 1.01 0.99stable? yes no yesbss -0.38 -1.07 -3.34


In Table 54 I report slightly different results, perhaps due torevisions in the data.


Postwar Reagan-Bush Clinton Bush IId -0.005549 0.012057 -0.020962 0.003688

Y N 0.073969 0.068409 0.056257 0.049039i 0.038409 0.080050 0.045525 0.028938(1+i)/(1+n) 0.966888 1.010895 0.989840 0.980838stable? yes no yes yesbss -0.167588 -1.106576 -2.063134 0.192481


“the Administration believes that an appropriatemedium-run goal is to balance the primary budget—the budget excluding interest payments on the debt.Including interest payments, this target will result intotal deficits of approximately 3 percent of GDP. Withreal GDP growth of about 2.5 percent per year andinflation of about 2 percent per year, nominal GDPgrowth will be about 4.5 percent per year in the longrun. Thus a target for the total deficit-to-GDP ratioof 3 percent implies that the debt-to-GDP ratio willstabilize at less than 70 percent.– ERP (2010, p.148)But if they will balance the primary budget, then thedebt will stabilize at a much higher level!


In the Postwar period we have stable debt-dynamics with thedebt slowly declining. By 1980 the debt was down to 32% ofGDP. If the average behavior over this period had beenmaintained, the government would have eventually boughtback all its debt and then accumulated private assets to thetune of 12% of GDP.


Note that during the Reagan and Bush administrations, wehave unstable budget dynamics. The fiscal policy isunsustainable: if maintained, the US must go bankrupt. Thisis a reasonable definition of budget crisis. We see theassociated rise in the debt-to-GDP ratio in the 1980s.


The budget crisis led policy makers to talk of balancing thebudget. This means equating revenues to total outlays, sothat the reported deficit is zero. Of course since outlaysinclude interest payments on the outstanding debt, thisrequires running a primary surplus. Graphically, we shift thebudget dynamics curve until it crosses the steady state locusat the current level of bonds.


Some economists believe that our emphasis on debt anddeficits is misplaced. Debt is just postponed taxation, andthese economists believe that consumers will set aside enoughsavings to pay these taxes when they are collected. Thisargument is associated with Robert Barro of HarvardUniversity. It has also been attributed to the 19th centuryEnglish economist David Ricardo, after whom it is named.The idea is that financing government expenditures with taxesor debt issue is equivalent in its economic effects, becauseconsumers will simply set aside funds for the postponed taxesrepresented by debt issue. Most simply, they can buy up thegovernment debt that is issued and then sell it as needed topay their future taxes.


During the 1980s, however, household savings did not seem toincrease in this way.


We have been ignoring the possibility that governmentborrowing can affect the interest rate at which the governmentcan borrow. The simplest way that this might happen is thatinterest rates may be driven up when the governmentcompetes for savings in the financial markets. Increases ingovernment debt may also mean that government debt is aless welcome addition to consumers’ portfolios. Finally,increases in government debt may also increase the perceivedrisk of holding government debt.


It is worth noting that slow growth and high interest rateswere common in the OECD countries in the 1980s. It is quitepossible that the contractionary monetary policy run by theUS was affecting international financial markets, which theassociated repercussions world-wide. Note that theinternational debt crisis erupted in 1982, as the rise in worldinterest rates led developing countries who had borrowedshort-term in private markets to be unable (or unwilling) tomeet their debt obligations.


Suppose we are in a situation of unstable debt dynamics and,as a response, the government changes its deficit policy sothat the deficit is reduced at higher levels of debt. You maythink of this as d = d − δb, with δ > 0.


Affect of ARRA 2009 on Deficit

Source: ERP (2010, fig 5.6)


Auerbach, Alan J. and William G. Gale. “An Update on theEconomic and Fiscal Crises: 2009 and Beyond (AnUpdate).

Barro, Robert J. (1989, Spring). “The Ricardian Approach toBudget Deficits.” Journal of Economic Perspectives 3(2),37–54.

Bernheim, B. Douglas (1989, Spring). “A NeoclassicalApproach to Budget Deficits.” Journal of EconomicPerspectives 3(2), 55–72.

Eisner, Robert (1989, Spring). “Budget Deficits and Reality.”Journal of Economic Perspectives 3(2), 73–94.

Farmer, Roger E. A. (2002). Macroeconomics (2nd ed.).Cincinnati, OH: South-Western.

Jones, Charles I. (2011). Macroeconomics (2 ed.). WWNorton.


Problems for Review I

See the problems in Farmer ch.14.

1 Explain the difference between the government debt, thereported deficit, and the primary deficit.

2 Graph the evolution of xt if xt = 1.05xt−1, xt = xt−1, orxt = 0.95xt−1.

3 Graph the evolution of the debt according to thedifference equation representing the George W. Bushadministration. What is the steady state level of debt?Are the adjustment dynamics stable.

4 Is monetary policy an important determinant of theevolution of government debt? Explain.


Problems for Review II

5 Suppose we are in a situation of unstable debt dynamicsand, as a response, the government changes its deficitpolicy so that the deficit is reduced at higher levels ofdebt. You may think of this as d = d − δb, with δ > 0.Can this be stabilizing? Illustrate graphically.

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