Advanced Macroeconomics

Transcription

1 Advanced Macroeconomics Chapter 5: Government: Expenditures and public finances Günter W. Beck University of Mainz December 14, 2010 Günter W. Beck () Advanced Macroeconomics December 14, / 16

2 Overview 1 The government budget constraint The nominal government budget constraint The real government budget constraint 2 Financing government expenditures: Tax finance 3 The sustainability of the fiscal stance 4 The stability and growth pact Günter W. Beck () Advanced Macroeconomics December 14, / 16

3 The government budget constraint The nominal government budget constraint The nominal government budget constraint The nominal government budget constraint is given by: P t g t + P t h t + (1 + R t ) B t = B t+1 + M t+1 + P t T t. (1) Notation: P t : Price level. g t : Real government expenditure. h t : Real transfers to households. B t : Government revenue from issuing bonds in period t 1. R t : Interest rate on government bonds issued in period t 1. M B t : Monetary base supplied at the start of period t ( M t+1 = M t+1 M t ). T B t : Total real taxes. Günter W. Beck () Advanced Macroeconomics December 14, / 16

4 The government budget constraint The real government budget constraint The real government budget constraint Dividing the nominal government budget constraint bhe price level P t yields: g t + h t + (1 + R t) B t P t = B t+1 P t + M t+1 P t + T t (2) g t + h t + (1 + R t ) b t = P t+1 P t B t+1 P t+1 + P t+1 P t M t+1 P t+1 M t P t + T t g t + h t + (1 + R t ) b t = (1 + π t+1) P t (b t+1 + m t+1 ) m t + T t g t + h t + (1 + R t ) b t = (1 + π t+1 ) (b t+1 + m t+1 ) m t + T t. P t Günter W. Beck () Advanced Macroeconomics December 14, / 16

5 Financing government expenditures: Tax finance Financing government expenditures: Tax finance Assumption: Consider a permanent increase in government spending in period t by g t which is financed by an increase in lump-sum taxes, T t. Since the increase is permanent we have: Moreover, we have: g t+s = g t = g, s 0. (3) T t+s = T t = T = g, s 0. (4) Since the additional government expenditures are financed bax increases no additional deficit is generated, i.e. b t+s = 0, s 0. Günter W. Beck () Advanced Macroeconomics December 14, / 16

6 Financing government expenditures: Tax finance Financing government expenditures: Tax finance The permanent tax increase will reduce the households available income, x T, from period t on. The households permanent income without the tax increase (denoted by Wt o ) is given by: W o t = (1 + R) a t + s=0 where we assumed that π = 0 and therefore r = R. ( ) 1 s [x t+s T t+s]. (5) 1 + R The households permanent income with the tax increase (denoted by Wt n ) is given by: W n t = (1 + R) a t + s=0 ( ) 1 s [x t+s T t+s T ] (6) 1 + R Günter W. Beck () Advanced Macroeconomics December 14, / 16

7 Financing government expenditures: Tax finance Financing government expenditures: Tax finance The households permanent income with the tax increase can be rewritten as follows: ( ) 1 s t = (1 + R) a t + [x t+s T t+s T ] = (7 s=0 1 + R ( ) 1 s ( ) 1 s = (1 + R) a t + [x t+s T t+s] s=0 1 + R T = s=0 1 + R ( ) 1 s 1 = (1 + R) a t + [x t+s T t+s] 1 + R 1 1 T = W n = (1 + R) a t + s=0 s=0 ( R 1+R ) s [x t+s T t+s] 1 + R R T. The change in households permanent income, W t = Wt o Wt n, is therefore given by: W t = Wt n Wt o = 1 + R T. (8) R Günter W. Beck () Advanced Macroeconomics December 14, / 16

8 Financing government expenditures: Tax finance Financing government expenditures: Tax finance Given the reduction in households permanent income their consumption will also fall. Denoting by ct o the households consumption without tax increases, by ct n the households consumption with tax increases and by c t the change in consumption then we have (given the assumptions of chapter 4.2): ( ) ( ) R R c t = ct n ct o = Wt n Wt o = (9) 1 + R 1 + R ( ) ( ) ( ( ) ) R R 1 + R = (Wt n Wt o ) = T 1 + R 1 + R R = T. = The tax-financed increase in permanent government spending leads to an equally-sized decrease in private consumption. Günter W. Beck () Advanced Macroeconomics December 14, / 16

9 Financing government expenditures: Tax finance Financing government expenditures: Tax finance The overall effect of the permanent increase in government spending on the economy (denoted by ) is given by: = c t + g t = T + T = 0. (10) = Permanent increase in government spending has no effect on the economy. Günter W. Beck () Advanced Macroeconomics December 14, / 16

10 The sustainability of the fiscal stance The sustainability of the fiscal stance Starting point: Nominal government budget constraint P t g t + P t h t + (1 + R t ) B t = B t+1 + M t+1 + P t T t. (11) Dividing both sides of this equation by nominal GDP, P t, yields: P t g t + P th t + (1 + R t) B t = B t+1 + M t+1 M t + P tt t. (12) P t P t P t P t P t P t P t Rearranging and simplifying yields: g t + h t + (1 + R t ) b t = T t + + B t+1 1 (1+π t+1 ) P 1 t+1 (1+γ t+1 ) +1 M t+1 1 (1+π t+1 ) P 1 t+1 (1+γ t+1 ) +1 + m t Günter W. Beck () Advanced Macroeconomics December 14, / 16

11 The sustainability of the fiscal stance The sustainability of the fiscal stance The just derived equation can be simplified as follows: g t + h t + (1 + R t ) b t = T t + y ( t bt+1 (1 + π t+1 ) (1 + γ t+1 ) + m ) t+1 m t where γ t+1 denotes the growth rate of real GDP between periods t and t + 1. The question we want to analyze in this section is whether a given government deficit, P t D t, is sustainable or not. The government deficit in a given period t is given by: P t D t = P t g t + P t h t + R t B t P t T t (M t+1 M t ). (13) Günter W. Beck () Advanced Macroeconomics December 14, / 16

12 The sustainability of the fiscal stance The sustainability of the fiscal stance Dividing the just derived equation by nominal GDP, P t, yields: D t = g t + h t + R t b t T t (1 + π t+1 ) (1 + γ t+1 ) m t+1 +1 m t. From the budget constraint we see that the right-hand side of this equation is given by: (14) g t + h t + R t b t T t (1 + π t+1 ) (1 + γ t+1 ) m t+1 +1 m t = (15) That is, we have: = (1 + π t+1 ) (1 + γ t+1 ) b t+1 +1 b t. D t = (1 + π t+1 ) (1 + γ t+1 ) b t+1 +1 b t. (16) Günter W. Beck () Advanced Macroeconomics December 14, / 16

13 The sustainability of the fiscal stance The sustainability of the fiscal stance Note: The difference between the actual deficit, D t and the interest payments on accumulated debt, R t B t, is called (nominal) primary deficit, P t d t, and is given by: P t d t = P t D t R t B t. (17) Assuming that inflation, π and output growth, γ are constant, the expression for D t becomes: D t = (1 + π) (1 + γ) b t+1 +1 b t (18) b t+1 +1 = = Interpretation? 1 (1 + π) (1 + γ) D t + 1 (1 + π) (1 + γ) b t (19) Günter W. Beck () Advanced Macroeconomics December 14, / 16

14 The stability and growth pact The stability and growth pact The stability and growth pact requires that D t 0.03 (20) and b t 0.60 (21) hold. Assuming that the deficit-gdp ratio remains constant over time the equation for the dynamics of the debt-gdp ratio (equation (19)) represents a stationary difference equation. Thus, the debt-gdp ratio will converge to a (constant) steady-state level and we will have in equilibrium: b t+1 +1 = b t = b t (22) Günter W. Beck () Advanced Macroeconomics December 14, / 16

15 The stability and growth pact The stability and growth pact Using the equation for the dynamics of the debt-gdp ratio we then obtain: b t+1 +1 = b y = (1 + π) (1 + γ) 1 b (1 + π) (1 + γ) y = b y = 1 D t 1 + (1 + π) (1 + γ) (1 + π) (1 + γ) 1 D (1 + π) (1 + γ) y + 1 b (1 + π) (1 + γ) y 1 D (1 + π) (1 + γ) y 1 D (1 + π) (1 + γ) 1 y. b t Since (1 + π) (1 + γ) 1 + π + γ we obtain: b y = 1 D π + γ y. (23) Günter W. Beck () Advanced Macroeconomics December 14, / 16

16 The stability and growth pact The stability and growth pact Implications of the analysis:assume that the current debt-gdp ratio is given by b ȳ. Then: If the debt-output ratio is kept constant over time and we have: 1 D π + γ y < b ȳ then the debt-gdp ratio will fall. If the debt-output ratio is kept constant over time and we have: 1 D π + γ y = b ȳ then the debt-gdp ratio will remain constant. If the debt-output ratio is kept constant over time and we have: 1 D π + γ y > b ȳ then the debt-gdp ratio will increase. (24) (25) (26) Günter W. Beck () Advanced Macroeconomics December 14, / 16