Macro Notes: Fiscal Deficits

Macro Notes: Fiscal Deficits Alan G. Isaac American University 2009

Any government, like any family, can for a year spend a little more than it earns. But you and I know that a 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 suddenly. Hemingway (in: The Sun Also Rises)

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

There are 10 11 stars in the galaxy. That used to be a huge number. But it s only a hundred billion. It s less than the national deficit! We used to call them astronomical numbers. Now we should call them economical 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 outlays and 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 face runaway deficits of almost $80 billion... Ronald Reagan, 1981 http://www.reagan.utexas.edu/archives/speeches/1981/20581c Reagan proved deficits don t matter. Dick Cheney, 2002, in response to Treasury Secretary 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 of the world.

Government Expenditure: Cross Country Variation Source: Jones (2008) Note: Euro = France, Germany, Spain, and Italy

Define the primary deficit: D p t = G t (Tx Tr) (1) The total deficit is the primary deficit plus the interest payments on government debt. D total t = D p t + ib t (2) Here B is the nominal supply of short term bonds, i is the short term nominal interest rate, and D p is the nominal primary deficit.

The annual evolution of nominal government debt: B t+1 B t + i t B t + D p t }{{} total deficit (3) We assume that bonds are very short maturity just to keep things simple: that way there is no change in value of government debt when the interest rate changes. (Another way we will keep things simple is by ignoring tax collections on the interest on government debt, which would show up in D p.)

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 foreign residents. (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 it compare to other nations? Until recently: Source: Jones (2011)

Debt-GDP Ratios The following graph makes things look worse, but it uses gross public debt. (E.g., it includes Fed and intragovernmental holdings of Treasury issue.) Source: http://www.usgovernmentspending.com/federal_debt_chart.html

Debt-GDP Ratios: Gross and Net Source: 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 the passage of time. The linkages between stocks and flows are a natural application of dynamic analysis. E.g., the stock of government debt changes as a result of the deficit (a flow variable).

We begin with a flow version of the government budget constraint: G t + Tr + ib t }{{} Uses = Tx t + B t + M t }{{} Sources (4) We can say the uses of funds equals the sources of funds. For simplicity, we will ignore seigniorage revenue for now. (That is, set M = 0.)

The primary deficit is the reported deficit less the governments net interest payments. The total deficit is therefore i t B t + D p t. Combining terms in B t 1 and assuming a constant interest rate we can rewrite this as B t+1 = (1 + i)b t + D p t (5) To keep things simple we have assume that bonds have a maturity of one period. 1 Also for simplicity, we assume that the interest rate is a constant. The result is an equation that links the evolution of the bond supply to its past value: a difference equation. 1 The maturity of a bond is the period from the date of issue to the date of redemption (when the principal must be repaid).

Difference equations: the past of a state variable determines its future values. Difference equations allow us to represent dynamics.

Recall D p is the primary deficit: the difference between non-interest government outlays and government revenues (Tx). Non-interest government outlays include government expenditures G plus non-interest transfer payments. The primary deficit differs from the reported deficit by the amount of the interest payments on government debt.

Reported vs. Primary Deficit for Postwar US Deficit Year Receipts Outlays Interest Reported Primary 1945 45.2 92.7 3.1 47.5 44.4 1992 1091.3 1381.6 199.6 290.3 90.7 2001 1991.1 1862.9 206.2-128.2-334.4 2002 1853.1 2010.9 170.9 157.8-13.1 2003 1782.3 2159.9 153.1 377.6 224.5 2004 1880.1 2292.9 160.2 412.8 252.6 2005 2153.6 2472.0 184.0 318.4 134.4 2006 2406.9 2655.1 226.6 248.2 21.6 2007 2568.0 2728.7 237.1 160.7-76.4 2008 2524.0 2982.6 252.8 458.6 205.8 2009 2105.0 3517.7 186.9 1412.7 1225.8 2010 2165.1 3720.7 187.8 1555.6 1367.8 2011 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 from the ERP Table B-80.

We see US economic history embodies a variety of experiences with deficits. In levels, the postwar period saw budgets that look balanced compared to recent history. We can see the deficit explosion in the 1980s and the corresponding acceleartion in debt accumulation. In this context the rising policy concern about federal deficits in the late 1980s and early 1990s is easy to understand. However data in levels fails to 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 unusual peace time events both in their size and their presistence, as a proportion of GDP we saw much larger debt and deficits in the wake of WWII. Still, there is an important difference. When the government produces a benefit for future generations, as when 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 seem to 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-gdp ratio gives a better sense of our ability to pay off our debt.

Recall our basic debt accumulation equation: B t+1 = D p t + (1 + i)b t (6) This equation embodies our basic debt dynamics: the accumulation of debt over time. This said that debt grows due to the primary deficit and due to interest rate payments on outstanding debt. We can also write this as B t+1 B t B t = Dp t + ib t B t = Dr t B t (7) The deficit to debt ratio is the growth rate of of debt. (So the debt to GDP ratio will stabilize when the deficit to debt ratio equals the growth rate of GDP.)

We now rewrite this as a fraction of GDP: B t+1 Y N t = Dp t Y N t + (1 + i) B t Y N t (8) Recall that Yt N dynamics as = (1 + Ŷ N )Y t 1, so we can rewrite our budget B t+1 Y N t = Dp t Y N t + 1 + i B t 1 + Ŷ N Yt 1 N Let b t = B t /Yt 1 N and let the primary deficit to GDP ratio be constant: b t+1 = d + 1 + i 1 + Ŷ b N t (10) (9)

This version of our debt dynamics equation also says that debt grows due to the primary deficit and due to interest rate payments on outstanding debt, but since we are looking at the debt-to-gdp ratio one additional factor enters: the rate of growth of GDP. Since we are focusing now on the debt-to-gdp ratio, when GDP grows this ratio shrinks and we need 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 if i > Ŷ N but shrinks if i < Ŷ N. That is, borrowing to make our interest payments adds to the debt, but this can be offset by GDP growth. On this observation hinges the entire question of whether budget policy is sustainable. If the debt-to-gdp ratio grows unbounded, eventually the interest payments on the debt will exceed the entire GDP. At this point (and obviously far before this) a government can be considered bankrupt: its tax base can no longer provide the revenues to meet its current interest obligations. 2 2 At this point we do not address the possibility of Ponzi scheme financing, where addtional borrowing would be undertaken to make the interest payments.

Alternative (ERP 2010, p.148) Analysis Write the flow constraint B t+1 = D p t + (1 + i)b t as (1 + Ŷ ) B t+1 Y N t+1 (since Yt+1 N = (1 + Ŷ )Y t N ) or = Dp t + ib t Y N t + B t Y N t (11) (1 + Ŷ N )b t+1 = d r t + b t (12) Set the reported deficit to GDP ratio constant and solve for b ss : (1 + Ŷ N )b ss = d r + b ss (13) so that b ss = d r Ŷ N (14)

Alternative (ERP 2010, p.148) Analysis Intuition: if the debt to GDP ratio is constant, then debt is growing at the same rate as GDP, and the growth rate of debt is the deficit to debt ratio. I.e., Ŷ N = d r /b in the steady state. Growth (Ŷ N ) Policy (d r ) Implied Debt (b ss ) 5% 1% 20% 4% 4% 100%

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

In figure 41 we show how a graph can be used to analyze debt dynamics. Note that both axes measure debt, but at different points in time. The horizontal axis is labeled b t and the vertical axis is b t+1. The graph includes a 45 deg line, along which b t+1 = b t. That is, along this line the debt-to-gdp ratio is not changing. We will refer to this as the steady-state locus. The graph also includes another line, which represents our debt dynamics. For any current level of debt b t, the height of the line is the debt next period. So given an initial level b 0 of the debt-to-gdp ratio, we can follow the evolution over time in this economy. We call the list of values taken over time the solution of the difference equation 10. Note that in the case we have drawn here, the debt-to-gdp ratio gradually approaches the steady state locus.

Stable Debt Dynamics b(t) b(0) b(1) b(2) b(t-1)

Recall that our debt dynamics were laid out in equation (10), which we repeat here for convenience. b t = d + 1 + i 1 + Ŷ N b t 1 Again we simplify by holding constant the primary deficit-to-gdp ratio, the interest rate, and the growth rate of GDP. So b t = d + ρb t 1 (15) Where ρ = (1 + i)/(1 + Ŷ N ).

In the steady state, the debt-to-gdp ratio is not changing. If the 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 + Ŷ N Ŷ N i d (17) Note for example that if Ŷ N i < 0 but d > 0, the steady state level of debt is negative.

We now ask if the steady state is stable. That is, if we are near the steady state, will me move toward it? Let us approach that question by subtracting the steady state value of b from both sides of equation 15 to get (b t d 1 ρ ) = ρ(b t 1 d 1 ρ ) (18) We see the distance of b from its steady state will be shrinking iff ρ < 1. Since interest rates and GDP growth rates are positive, we are interested in whether ρ < 1. Equivalently, for a stable steady state we need i < Ŷ N.

Unstable Debt Dynamics b(t) b(0) b(1) b(2) b(t-1)

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

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

These changes in the US have been associated (e.g., by Farmer (2002,p.320)) with two policy events: the replacement of Arthur Burns by Paul Voker as chairman of the Fed in August 1979 (which led to a radical revision of monetary policy that October), and the Omnibus Budget Reconciliation Act of 1993. The first event clearly led to a surge in interest rates. The uniqueness of the second event is more questionable however, since the 1980s and 1990s saw repeated legislative 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 $12B in 1986) 1987 PL 100-202, 203 Omnibus Reconciliation Act (various outlay reductions) 1990 PL 101-508 Omnibus Reconciliation Act (tax hike for high income households) 1993 PL 103-66 Omnibus Budget Reconciliation Act (increased taxes and lower spending) 1997 PL 105-33 Omnibus Reconciliation Act (cuts in Medicare and disretionary spending)

Despite all this legislation, it was not until 1993 that the budget situation clearly moved toward long term improvement. Part of the improvement was of course due to the strong growth during the Clinton administration, which improved federal 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, Ŷ N, and i. Table?? reports the results of Farmer (2002). 3 3 In the last line of this table, I have corrected Farmer s value for the Clinton era as reported in his Figure 14.8, which (based on his data) misplaced the decimal point. These results are illustrated by Farmer figures 14.6, 14.7, and 14.8.

Stability by Period: Farmer s Results Postwar Reagan-Bush Clinton d -1.2% 0.7% -1.9% Ŷ N 7.5% 6.89% 5.5% i 4.1% 7.5% 4.9% (1 + i)/(1 + Ŷ N ) 0.97 1.01 0.99 stable? yes no yes b ss -0.38-1.07-3.34

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

Postwar Reagan-Bush Clinton Bush II d -0.005549 0.012057-0.020962 0.003688 Ŷ N 0.073969 0.068409 0.056257 0.049039 i 0.038409 0.080050 0.045525 0.028938 (1+i)/(1+n) 0.966888 1.010895 0.989840 0.980838 stable? yes no yes yes b ss -0.167588-1.106576-2.063134 0.192481

the Administration believes that an appropriate medium-run goal is to balance the primary budget the budget excluding interest payments on the debt. Including interest payments, this target will result in total deficits of approximately 3 percent of GDP. With real GDP growth of about 2.5 percent per year and inflation of about 2 percent per year, nominal GDP growth will be about 4.5 percent per year in the long run. Thus a target for the total deficit-to-gdp ratio of 3 percent implies that the debt-to-gdp ratio will stabilize at less than 70 percent. ERP (2010, p.148) But if they will balance the primary budget, then the debt will stabilize at a much higher level!

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

Note that during the Reagan and Bush administrations, we have unstable budget dynamics. The fiscal policy is unsustainable: if maintained, the US must go bankrupt. This is a reasonable definition of budget crisis. We see the associated rise in the debt-to-gdp ratio in the 1980s.

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

Some economists believe that our emphasis on debt and deficits is misplaced. Debt is just postponed taxation, and these economists believe that consumers will set aside enough savings to pay these taxes when they are collected. This argument is associated with Robert Barro of Harvard University. It has also been attributed to the 19th century English economist David Ricardo, after whom it is named. The idea is that financing government expenditures with taxes or debt issue is equivalent in its economic effects, because consumers will simply set aside funds for the postponed taxes represented by debt issue. Most simply, they can buy up the government debt that is issued and then sell it as needed to pay their future taxes.

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

We have been ignoring the possibility that government borrowing can affect the interest rate at which the government can borrow. The simplest way that this might happen is that interest rates may be driven up when the government competes for savings in the financial markets. Increases in government debt may also mean that government debt is a less welcome addition to consumers portfolios. Finally, increases in government debt may also increase the perceived risk of holding government debt.

It is worth noting that slow growth and high interest rates were common in the OECD countries in the 1980s. It is quite possible that the contractionary monetary policy run by the US was affecting international financial markets, which the associated repercussions world-wide. Note that the international debt crisis erupted in 1982, as the rise in world interest rates led developing countries who had borrowed short-term in private markets to be unable (or unwilling) to meet their debt obligations.

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

Source: Jones (2011)

Source: Jones (2011)

Affect of ARRA 2009 on Deficit Source: ERP (2010, fig 5.6)

Source: Jones (2009)

Source: Jones (2009)

Auerbach, Alan J. and William G. Gale. An Update on the Economic and Fiscal Crises: 2009 and Beyond (An Update). Barro, Robert J. (1989, Spring). The Ricardian Approach to Budget Deficits. Journal of Economic Perspectives 3(2), 37 54. Bernheim, B. Douglas (1989, Spring). A Neoclassical Approach to Budget Deficits. Journal of Economic Perspectives 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.). WW Norton.

Problems for Review I See the problems in Farmer ch.14. 1 Explain the difference between the government debt, the reported deficit, and the primary deficit. 2 Graph the evolution of x t if x t = 1.05x t 1, x t = x t 1, or x t = 0.95x t 1. 3 Graph the evolution of the debt according to the difference equation representing the George W. Bush administration. What is the steady state level of debt? Are the adjustment dynamics stable. 4 Is monetary policy an important determinant of the evolution of government debt? Explain.

Problems for Review II 5 Suppose we are in a situation of unstable debt dynamics and, as a response, the government changes its deficit policy so that the deficit is reduced at higher levels of debt. You may think of this as d = d δb, with δ > 0. Can this be stabilizing? Illustrate graphically.