6. Budget Deficits and Fiscal Policy

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1 Prof. Dr. Thomas Steger Advanced Macroeconomics II Lecture SS Budget Deficits and Fiscal Policy Introduction Ricardian equivalence Distorting taxes Debt crises

2 Introduction (1) Ricardian equivalence Keynesian theory holds that government spending financed by issuing bonds has a larger impact on aggregate demand than tax-financed government spending. New Classical economists argue that rational, forward-looking households do understand that issuing bonds today requires to raise taxes tomorrow such that the financing scheme is neutral w.r.t. consumption. We will look at the critical assumptions underlying this neutrality proposition and summarize the main empirical findings. Debt crises The occurrence of debt crisis remains an important topic. The answer to the following question appears especially interesting: Can economic theory help understanding causes of debt crises? Moreover, is a debt crises the result of bad fundamentals (hence unavoidable?) or is there an element of self fulfilling beliefs? 2

3 Ricardian equivalence (1) The Ricardian equivalence theorem was formulated by the British neoclassical economist David Ricardo (1817). The new classical economist Robert Barro (1974) forcefully argued that the Ricardian equivalence theorem is worthy of professional attention and yields important policy implications. Sketch of Ricardian Equivalence Theorem Proposition: For a given time path of government spending the particular method used to finance these expenditures (taxation or debt) does not affect real consumption, real investment, and real output. Corollary: Under Ricardian equivalence, government bonds held by private agents should not be counted as net wealth since it is exactly matched by future liabilities (expected tax increases). 3

4 Ricardian equivalence (2) Basic assumptions Consider a world that lasts for two periods (present,1, and future, 2) There is perfect foresight on the part of households and government. The capital market is perfect. The periodic budget constraints are given by 0 A 0 (stock variable, end of period) period 1 C 1 (flow variable) period C 2 A 1 A 2 From (2) one gets A 1 =(C 2 (1 τ 2 )Y 2 )/(1+r), noting (1) gives the intertemporal budget constraint 4

5 Ricardian equivalence (3) The government s periodic budget constraints read as follows The government does not issue money and is restricted to end without debt, i.e. B 2 =0. The government can finance government expenditures by issuing bonds or by levying taxes. Solving (4) w.r.t. B 1 gives B 1 =(τ 2 Y 2 G 2 )/(1+r). Plugging this into (3) and rearranging gives This is the intertemporal budget constraint of the government. Since government bonds are the only financial asset in the model economy, household lending (borrowing) can only take the form of positive (negative) holdings of government bonds. Hence, equilibrium in the financial market implies A i =B i for i=0,1,2. 5

6 Ricardian equivalence (4) The consolidated budget constraint of the whole economy results by merging the intertemporal budget constraints of the private sector and the government. Solving (5) w.r.t. (1+r)B 0 gives (1+r)B 0 =τ 1 Y 1 G 1 +(τ 2 Y 2 G 2 )/(1+r). Plugging the result into the household s intertemporal budget constraint yields Borrowing today requires repayment tomorrow and future repayment accordingly requires future tax revenues. Hence, rational, forward looking households take the consolidated budget constraint into account when deciding on optimal consumption plans. The consolidated intertemporal budget constraint says that the PDV of consumption {C 1,C 2 } must equal the PDV of income net of government expenditures. The time path of taxes {τ 1,τ 2 } does not show up implying that the way in which the government finances its expenditures has no effect on real consumption. 6

7 Ricardian equivalence (5) To fully understand the economic intuition behind Ricardian equivalence, we investigate the household s saving decision. The household is assumed to solve the following problem The associated Lagrangian and the first order conditions are given by 7

8 Ricardian equivalence (6) Combining FOC1 and FOC2 gives the Euler equation The Euler equation determines the optimal rate of change of consumption. The optimal levels of C 1 and C 2 can be obtained as follows Notice that the Euler equation implies C 2 =C 1 (1+r)/(1+ρ) and C 1 =C 2 (1+ρ)/(1+r). Combine these expressions with the consolidated budget constraints 8

9 Ricardian equivalence (7) Household saving in the 1 st period is as follows Optimal saving is affected by the tax rate τ 1. Consider the following Ricardian experiment : The government reduces the tax rate in the first period (dτ 1 <0) but keeps goods demand {G 1, G 2 } unchanged. Private saving changes according to ds 1 =-Y 1 dτ 1 >0. The intertemporal budget constraint (5) implies A reduction in the tax rate today requires, via the intertemporal budget constraint, an increase in the tax rate tomorrow (holding {G 1, G 2 } unchanged). The household increases its saving such that it is able to repay the associated tax increase tomorrow, i.e. ds 1 = Y 1 dτ 1 =(Y 2 dτ 2 )/(1+r)>0. Hence, the expansive fiscal impulse dτ 1 <0 is offset by a reduction in C 1! 9

10 Distorting taxes (1) There are a number of simplifying assumptions which are indeed critical with regard to the Ricardian equivalence result. Even worse, most of these simplifying assumptions are critical and appear fairly unrealistic. Here, we consider the consequences of distorting taxes. Assume that non-interest income is exogenous but that there is a comprehensive income tax, and that interest income is taxable. The household s periodic budget constraints now read (noting A i =B i for i=0,1,2) Solving the 2 nd constraint w.r.t. B 1 and substituting into the 1 st constraint yields the intertemporal budget constraint 10

11 Distorting taxes (2) The periodic budget constraint of the government reads Solving the 2 nd constraint w.r.t. B 1 and substituting into the 1 st constraint yields the intertemporal budget constraint Finally, solving the preceding equation w.r.t. (1+(1 τ 1 )r))b 0 and substituting the result into the household s intertemporal budget constraint gives the consolidated budget constraint The income tax τ 2 does not drop out (τ 1 does not appear because it operates like a lump sum tax). The optimal consumption plan is affected by the timing of taxation. The tax rate in the 2 nd period changes the intertemporal prices of consumption now versus tomorrow and, hence, distorts the saving decision. 11

12 Summary and conclusion Some critical assumption underlying the Ricardian equivalence proposition Altruistic connection between generations in an infinite horizon context (such that a bond issued today is not viewed as wealth due to the future tax burden) Taxes do not affect allocations (intertemporal consumption, leisure versus working time) The capital market is perfect. Households are completely rational, not myopic, endowed with the cognitive power to calculate optimal consumption plans, and have all relevant information available. Notice that for Ricardian equivalence to hold, theses assumptions must be satisfied simultaneously; for critical comments, see Akerlof (AER, 2007). Sketch of empirical evidence The empirical evidence appears inconclusive. Seater (JEL, 1993) concludes that Ricardian equivalence is a good approximation, while Bernheim (NBER Macroeconomics Annual, 1987) comes to the conclusion that it is at variance with the facts. 12

13 A model of debt crises (1) A stylized model of debt crises is setup which rests on the following basic assumptions Government has a quantity D of maturing liabilities (debt). It has no funds immediately available and wants to roll the debt over (i.e. issue new bonds to repay principal and interest). Next period it will be obtaining tax revenues T and so wants the investors to hold the debt for one period. Tax revenues T is random and described by the continuous CDF F(T), described below. Government offers an interest factor of R. Two simplifying assumptions maturing Liabilities D 1 =RD 0 debt rollover, i.e. issuing new bonds: D 1 timing of events current period tax revenues are realized: T debt repay: RD 1 or complete default Default is all or nothing: if the government cannot pay RD, it repudiates the debt entirely. Investors are risk neutral and the risk-free interest factor R is independent of R and D. 13

14 A model of debt crises (2) Capital market equilibrium requires Notice that investors are assumed to be risk neutral. We distinguish between the expected probability of default π e and the fundamentally warranted probability of default π fw, to be explained bellow. Overall equilibrium requires that π e =π fw. R=

15 A model of debt crises (3) Tax revenues are uncertain and distributed according to a bell-shaped density function f(t). The (fundamentally warranted) probability of default can be described by π fw =P(T<RD). Let T min denote the smallest possible value for T and T max the largest possible value. For RD<T min we have P(T<RD)=0. For RD>T max we have P(T<RD)=1. Given f(t) the probability of default π fw =P(T<RD) in response to RD is S-shaped. Moreover, given f(t) and holding D fix, the probability of default π fw =P(T<RD) in response to R is S-shaped too. 15

16 A model of debt crises (4) B A B A C Equilibrium requires that two conditions must hold simultaneously: Condition 1: The interest factor on government debt R makes the investors willing to purchase the debt given the expected probability of default π e, i.e. π e =(R-R)/R. Condition 2: The fundamentally warranted probability of default π fw is the probability that tax revenues are insufficient to pay off the debt given the interest factor R, i.e. π fw =P(T<RD). The intersections of the two curves π e =(R R)/R and π fw =P(T<RD) describe two equilibria. There is a third equilibrium, namely R=, π=1. If investors refuse to purchase the debt at any R, the probability of default is π fw =1. If π e =1, investors refuse to purchase the debt at any interest factor. Equilibrium A and C are stable, while equilibrium B is unstable (reasoning?). Multiplicity of equilibria implies that there can be a selffulfilling element of default. Assume that the economy is in B initially. Investors now start to believe that the probability of default has increased ( a rating agency has published new figures ), i.e. π e increases. Investors demand a higher interest factor, RD increases, such that π fw does indeed go up. The process converges to C where the government pays a very high interest rate and default occurs. 16

17 A model of debt crises (5) A A C Assume the economy is in the good equilibrium, point A, initially. Assume further that the risk-free interest factor R increases (USA start to borrow extensively). At first the equilibrium changes smoothly. An increase in R leads to a gradual increase in R and π. As R increase further, however, drastic changes may occur. The (good) equilibrium, characterized by combination of low R and π, collapses and the economy moves to the (bad) equilibrium (R=, π=1). The equilibrium probability of a default results from the interaction between fundamentals, as captured by R, D, and E(T) and self fulfilling beliefs. 17

18 Notation and abbreviations Notation A i B i C i G i r R R S i T Y i λ π e π fw Ω ρ τ i assets in period i debt in period i consumption in period i government purchases in period i interest rate interest factor offered by government risk-free interest factor Household saving in period i tax revenue income in period i Lagrangian multiplier expected probability of default fundamentally warranted probability of default wealth time preference rate tax rate in period i Abbreviations CDF cumulative distribution function FOC first-order conditions PDV present discounted value w.r.t. with respect to 18

. In this case the leakage effect of tax increases is mitigated because some of the reduction in disposable income would have otherwise been saved.

. In this case the leakage effect of tax increases is mitigated because some of the reduction in disposable income would have otherwise been saved. Chapter 4 Review Questions. Explain how an increase in government spending and an equal increase in lump sum taxes can generate an increase in equilibrium output. Under what conditions will a balanced

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