Macroeconomics Prof. Juan Gabriel Rodríguez

1. MacroeconomicsProf. Juan Gabriel Rodríguez Chapter 3 Budget deficit and sustainability of debt

2. Question What will happen to an economy if during a crisis the government increases public spending (or reduces taxes) to boost that economy? [What will happen to debt over time? Will the government need to increase taxes later?]

3. So far… So far we have dealt with a static model where taxes and government spending are fixed. However, - Intertemporal issues must be considered! - Long-run effects of government deficits and debt?? - Taxes and government spending are endogenous (public deficit is anti-cyclical)

4. So far… Causes of government deficits: • Economic cycle • Weakness of the fiscal system: tax evasion, black economy, corruption, debt financial burden. • Investments to increase physical capital K (that increase future growth): infrastructures, research, health, education,… • Unproductive spending (that do not increase future growth…): national defense.

5. The Government Budget Constraint • The budget deficit in year t equals: • Bt-1 is (real) government debt at the beginning of year t ; r is the real interest rate (i-), which we shall assume to be constant here. Thus rBt-1 equals the real interest payments on the government debt in year t. • Gt is (real) government spending during year t. • Tt is (real) taxes minus transfers during year t. In words: The budge deficit equals spending, including interest payments on the debt, minus taxes net of transfers.

6. The Government Budget Constraint Real interest payments rather than actual interest payments. The correct measure of the deficit is sometimes called the inflation-adjusted deficit. The difference between spending and taxes, Gt – Ttis called the primary deficit (equivalently, Tt – Gt is called the primary surplus).

7. The Government Budget Constraint The government budget constraint states that the change in government debt during year t is equal to the deficit during year t (the deficit flow causes the variation of the debt stock): Using the definition of the deficit Therefore:

8. Primary Deficit The Government Budget Constraint • Interest payments • Primary deficit Change in the debt

9. The Government Budget Constraint Let’s look at the implications of a 1-year decrease in taxes (or, equivalently, an increase in government spending) for the path of debt and future taxes. We start with a balanced budget (G0 – T0=0), and end the year with the government decreasing taxes by 1 for 1-year. What happens thereafter?

10. The Government Budget Constraint Or equivalently, Task: full repayment of debt in a given number of years - Will the government need to increase taxes or decrease spending later? Yes… - If so, by how much? It will depend on the period the repayment takes

11. The Government Budget Constraint • Full Repayment in Year 2 Replacing B2=0 and B1=1, and rearranging: To repay the debt fully in year 2, the government must run a primary surplus equal to (1+r).

12. The Government Budget Constraint If the debt is fully repaid during year 2, the decrease in taxes of 1 in year 1 requires an increase in taxes equal to (1+ r ) in year 2. (b) If the debt is fully repaid during year 5, the decrease in taxes of 1 in year 1 requires an increase in taxes equal to (1 + r)4 during year 5.

13. The Government Budget Constraint • Full Repayment in Year t Debt at the end of year t1 is given by: In year t, when the debt is repaid, the budget constraint is: Debt at the end of year t equals zero: which implies that the necessary surplus in year t to repay the debt must be:

14. The Government Budget Constraint Conclusions: • If government spending is unchanged, a decrease in taxes must eventually be offset by an increase in taxes in the future. • The longer the government waits to increase taxes, or the higher the real interest rate, the higher the eventual increase in taxes.

15. The Government Budget Constraint Task: debt stabilization in Year t (B1=B2=…=1) • From , the budget constraint for year 2 is • Under our assumption that debt is stabilized in year 2, B2 = B1 = 1. Replacing in the preceding equation: • Reorganizing and bringing G2 – T2 to the left side:

16. The Government Budget Constraint If the debt is stabilized from year 2 on, then taxes must be permanently higher by r from year 2 on.

17. The Government Budget Constraint • The legacy of past deficits is higher government debt. • To stabilize the debt, the government must eliminate the deficit. • To eliminate the deficit, the government must run a primary surplus equal to the interest payments on the existing debt. This requires higher taxes forever. Debt Stabilization in Year t

18. The Government Budget Constraint However: In an economy in which output grows over time, it makes sense to focus on the ratio of debt to output (Bt/Yt).

19. The Government Budget Constraint

20. The change in the debt ratio over time is equal to The first term is the difference between the real interest rate and the (real) growth rate times the initial debt ratio. If r>g… If r<g… The second term is the ratio of the primary deficit to GDP. The Government Budget Constraint

21. The Government Budget Constraint The increase in the ratio of debt to GDP will be larger: • the higher the real interest rate, • the lower the growth rate of output, • the higher the initial debt ratio, • the higher the ratio of the primary deficit to GDP.

22. The Spanish Case • In Spain: • Large primary deficits: significant increases on government spending and decreases on taxes revenue (caused by the economic crisis). • Problem: • High r because the sovereign debt crisis • Low or negative rates of growth Spain need to reduce its primary deficit to decrease the ratio of debt to GDP…

23. 4 (T-G)/GDP 2 0 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 -2 -4 -6 -8 -10 -12 The Spanish Case

24. The Spanish Case • 2007 (S-I) = (G-T) + (X-Q) -13,0 = -2,2 + -9,8 • 2008 (S-I) = (G-T) + (X-Q) -5,4 = +4,1 + - 9,5 • 2009 (S-I) = (G-T) + (X-Q) +6,1 = +11,2, + - 5,1 • 2011(prev) (S-I) = (G-T) + (X-Q) +2,2 = +6,3 + - 4,1

25. The Spanish Case

26. 80 70 60 50 40 30 Debt/GDP 20 10 0 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 The Spanish Case

27. Relevance for Fiscal Policy Ricardian Equivalence • The Ricardian Equivalence (also known as the Ricardo-Barro proposition), is the argument that, once the government budget constraint is taken into account, neither deficit nor debt has an effect on economic activity. • Consumers do not change their consumption in respond to a tax cut if the present value of after-tax labor income is unaffected. The effect of lower taxes today is cancelled out by higher taxes tomorrow. • Put it in a different way: The decrease in public saving is offset by an equal increase in private saving. However, Ricardian equivalence is likely to fail because future tax increases can be distant and their timing uncertain. So, budget deficits have important effects on activity: - Short-run: larger deficits lead to higher demand and output. - Long-run: higher debt lowers capital accumulation and output.

28. Relevance for Fiscal Policy The fact that budget deficits increase during recessions and decrease during booms causes budget deficit to be called automatic stabilizer. • Another issue • There are two good reasons to run deficits during wars: • The first is distributional—Deficit finance is a way to pass some of the burden of the war to those alive after the war, and it seems only fair for future generations to share in the sacrifices the war requires. • The second is more narrowly economic—Deficit spending helps reduce tax distortions.

29. Relevance for Fiscal Policy • First, with government spending sharply up, there will be a very large increase in the demand for goods, while, increases in taxes will reduce consumption sharply. • Second, high tax rates will lead to high economic distortions. People will work less, and engage in illegal, untaxed activities. That is why tax smoothing (maintain a relatively constant tax rate) seems to be a good idea: large deficits when government spending is high and small surpluses the rest of the time.

30. Relevance for Fiscal Policy The higher the ratio of debt to GDP, the larger the potential for catastrophic debt dynamics: Expectations of higher and higher debt give a hint that a problem may arise, which will lead to the emergence of the problem, thereby validating the initial expectations (self-fulfilling expectations).