The Fallacy of Fiscal Discipline

Transcription

1 The Fallacy of Fiscal Discipline Paolo Canofari a,b,c, Alessandro Piergallini b, Giovanni Piersanti b,c a Luiss School of European Political Economy b University of Rome Tor Vergata c University of Teramo Università La Sapienza di Roma December 2016 (Università La Sapienza di Roma) Fiscal Sustainability December / 23

2 Motivations Debt-GDP ratio exhibits a stock variable measured relative to a ow variable. (Università La Sapienza di Roma) Fiscal Sustainability December / 23

3 Motivations Debt-GDP ratio exhibits a stock variable measured relative to a ow variable. This paper considers wealth-based sustainability index of government debt. (Università La Sapienza di Roma) Fiscal Sustainability December / 23

4 Motivations Debt-GDP ratio exhibits a stock variable measured relative to a ow variable. This paper considers wealth-based sustainability index of government debt. The index has been derived from a baseline endougenous growth model. (Università La Sapienza di Roma) Fiscal Sustainability December / 23

5 Motivations Debt-GDP ratio exhibits a stock variable measured relative to a ow variable. This paper considers wealth-based sustainability index of government debt. The index has been derived from a baseline endougenous growth model. We compute the index from 1999 to 2013 according to the theoretical setup. (Università La Sapienza di Roma) Fiscal Sustainability December / 23

6 Motivations Debt-GDP ratio exhibits a stock variable measured relative to a ow variable. This paper considers wealth-based sustainability index of government debt. The index has been derived from a baseline endougenous growth model. We compute the index from 1999 to 2013 according to the theoretical setup. Results show that scal position is sustainable for Germany and Italy, weakly and strongly unsustainable for France and Japan respectivelly. (Università La Sapienza di Roma) Fiscal Sustainability December / 23

7 Literature Indicators assessing scal sustainabity are based on the time path of the Debt-GDP ratio:miller (1983), Buiter (1985), Blanchard (1990), and Buiter, Corsetti and Rubini (1993). (Università La Sapienza di Roma) Fiscal Sustainability December / 23

8 Literature Indicators assessing scal sustainabity are based on the time path of the Debt-GDP ratio:miller (1983), Buiter (1985), Blanchard (1990), and Buiter, Corsetti and Rubini (1993). Tests, are suggested, for example, by Hamilton and Flavin (1986), Trehan and Walsh (1988), and Bohn (1998, 2008). (Università La Sapienza di Roma) Fiscal Sustainability December / 23

9 Literature Indicators assessing scal sustainabity are based on the time path of the Debt-GDP ratio:miller (1983), Buiter (1985), Blanchard (1990), and Buiter, Corsetti and Rubini (1993). Tests, are suggested, for example, by Hamilton and Flavin (1986), Trehan and Walsh (1988), and Bohn (1998, 2008). Marini and Piergallini (2008) provide a literature review on the two approaches. (Università La Sapienza di Roma) Fiscal Sustainability December / 23

10 Policy Implications Once privete wealth has been taken into consideration the results on scal sustainability are much di erent respect to the common windsom. (Università La Sapienza di Roma) Fiscal Sustainability December / 23

11 Policy Implications Once privete wealth has been taken into consideration the results on scal sustainability are much di erent respect to the common windsom. Fiscal rules such as those enshrined in the Fiscal Compact in the European Union can be considered misleading. (Università La Sapienza di Roma) Fiscal Sustainability December / 23

12 Policy Implications Once privete wealth has been taken into consideration the results on scal sustainability are much di erent respect to the common windsom. Fiscal rules such as those enshrined in the Fiscal Compact in the European Union can be considered misleading. The sustainability results here obtained for both Germany and Italy are instructive. (Università La Sapienza di Roma) Fiscal Sustainability December / 23

13 Policy Implications Once privete wealth has been taken into consideration the results on scal sustainability are much di erent respect to the common windsom. Fiscal rules such as those enshrined in the Fiscal Compact in the European Union can be considered misleading. The sustainability results here obtained for both Germany and Italy are instructive. Incorporating agents wealth in the formulation of budgetary policy indicators turns out to be essential to guarantee logical consistency in monitoring scal sustainability. (Università La Sapienza di Roma) Fiscal Sustainability December / 23

14 The Model We consider a model à la Bruce and Turnovsky (1999). The representative household s utility function is U = Z t 1 σ (CG ε C ) σ e β(v t) dv, ε > 0, < σ < 1, εσ < 1, 1 > σ (1 + ε) (Università La Sapienza di Roma) Fiscal Sustainability December / 23

15 The Model Household faces the following budget constraint: W K + B = rb + (1 τ) Y (1 + {) C T, (2) The production function is described by Y = AG α I K 1 α α GI = A K, 0 α 1, (3) K (Università La Sapienza di Roma) Fiscal Sustainability December / 23

16 The Model The economy-wide resource constraint is The government budget constraint is K = Y C G, (4) B = rb + G τy {C T. (5) (Università La Sapienza di Roma) Fiscal Sustainability December / 23

17 Household s optimization problem subject to max Z t 1 σ (CG ε C ) σ e β(v t) dv K + B = rb + (1 τ) AG α I K 1 α (1 + {) C T. (Università La Sapienza di Roma) Fiscal Sustainability December / 23

18 Household s optimization problem The Lagrangean for this problem is de ned as L = 1 σ (CG ε C ) σ e +λe β(v β(v t) t) rb + (1 τ) AG α I K 1 α (1 + {) C T K + B (Università La Sapienza di Roma) Fiscal Sustainability December / 23

19 Household s optimization problem The conditions for an optimum are L C = 0 =) (CG C ε ) σ 1 GC ε = λ (1 + {), λ + βλ = L K =) λ + βλ = L B =) λ + β = A (1 λ α) (1 τ) λ λ + β = r. α GI, K (Università La Sapienza di Roma) Fiscal Sustainability December / 23

20 Household s optimization problem Combining the last two equations, we can express these conditions as (CG ε C ) σ 1 G ε C = λ (1 + {), (6a) α GI r = A (1 α) (1 τ) = β K In addition, the transversality conditions λ λ. (6b) lim λbe (v t) = lim λke (v t) = lim λwe (v t) = 0 (6c) v! v! v! (Università La Sapienza di Roma) Fiscal Sustainability December / 23

21 Household s optimization problem Using (6b) and di erentiating (6a) with respect to time yields the growth relationship C (σ 1) C + (εσ) G C = β r; (7a) G C the rst equality of (6b) implies that the interest rate is given by α GI r = A (1 α) (1 τ). K (7b) Thus, a rise in (G I /K ) increases the equilibrium rate of interest r. Finally, using (7b), we can express the aggregate output as r Y = K. (8) (1 α) (1 τ) (Università La Sapienza di Roma) Fiscal Sustainability December / 23

22 Balanced Growth Assume that the government sets its expenditures as constant shares of output, i.e., set G C = γ C Y, G I = γ I Y, 0 < γ C, γ I < 1; (9) assume also that along the balanced growth path all real variables grow at the same constant rate g. Thus, Y Y = K K = B B = W W = C C = G C G C = G I G I g. (10) Combining (10) with (7a) shows that the equilibrium growth rate is given by r β g = 1 σ (1 + ε). (11) (Università La Sapienza di Roma) Fiscal Sustainability December / 23

23 Balanced Growth Also, using the aggregate production function and G I = γ I Y yields G I K = (Aγ I ) 1 1 α, which, substituted in (7b), allows the interest rate to be rewritten as r = A (1 α) (1 τ) (Aγ I ) α 1 α. (7b ) Next, dividing (4) by K and using (8), we can rewrite the aggregate resource constraint as K K g =r (1 γ C γ I ) (1 α) (1 τ) C K, C K ϕ = r (1 γ C γ I ) (1 α) (1 τ) g. (12) (Università La Sapienza di Roma) Fiscal Sustainability December / 23

24 Balanced Growth Finally, dividing (2) by W and using (8), and letting T be equal to zero for simplicity,we obtain K W ω = r g (1 + {) ϕ r 1 + αω C W η = rα, (13a) 1 α g 1 α. (13b) (1 + {) (Università La Sapienza di Roma) Fiscal Sustainability December / 23

25 Long-run Sustainability of Fiscal Policy The value of this government bond is 1/r and the value of the outstanding debt is B = b/r, where b is the number of outstanding bonds. With r constant this also implies B b = r. Using (8), (9), and (12), rewrite now the government budget constraint (5) as b r = b + γc + γ I τ rk {ϕk T. (13) (1 α) (1 τ) Next, integrate (13) over the range [t, ), to obtain Z T v e r (v t) dv = b Z t r + γc + γ r I τ t (1 α) (1 τ) t {ϕ K t e (r g ) (v t) dv (14) (Università La Sapienza di Roma) Fiscal Sustainability December / 23

26 Long-run Sustainability of Fiscal Policy Solving (14) under the transversality conditions (6c), and dividing through by the size of the current wealth leads to γc + γ Z T v e r (v t) F dv = (b r I τ {ϕ t /r) (1 α) (1 τ) + ω, (15) t W t r g W t where the transversality conditions implies We call F a sustainability index of scal policy. r > g, (16) (Università La Sapienza di Roma) Fiscal Sustainability December / 23

27 Long-run Sustainability of Fiscal Policy The index provides a dynamic scoring of government debt by which we can assess a country s scal position as follows. When F 0 scal policy is said to be sustainable. When 0 < F < (b t /r) /W t scal policy is said to be weakly sustainable. When F > (b t /r) /W t scal policy is said to be unsustainable. (Università La Sapienza di Roma) Fiscal Sustainability December / 23

28 Empirical Results We calculate the index F given for the post-1999 period, focusing on countries in which r > g. (Università La Sapienza di Roma) Fiscal Sustainability December / 23

29 Empirical Results We calculate the index F given for the post-1999 period, focusing on countries in which r > g. We obtain the nominal interest rate series by dividing interest payments for period t over the stock of nominal debt at the end of period t 1, consistently with Bohn (2008). (Università La Sapienza di Roma) Fiscal Sustainability December / 23

30 Empirical Results We calculate the index F given for the post-1999 period, focusing on countries in which r > g. We obtain the nominal interest rate series by dividing interest payments for period t over the stock of nominal debt at the end of period t 1, consistently with Bohn (2008). Since budgetary forecasts contained the IMF World Economic Outlook are available up to 2021, the computation of the sustainability index uses averages of scal variables over nine years. (Università La Sapienza di Roma) Fiscal Sustainability December / 23

31 Empirical Results We calculate the index F given for the post-1999 period, focusing on countries in which r > g. We obtain the nominal interest rate series by dividing interest payments for period t over the stock of nominal debt at the end of period t 1, consistently with Bohn (2008). Since budgetary forecasts contained the IMF World Economic Outlook are available up to 2021, the computation of the sustainability index uses averages of scal variables over nine years. The Figure shows the behavior of the scal indicator for Germany, Italy, France and Japan. (Università La Sapienza di Roma) Fiscal Sustainability December / 23

32 Empirical Results France Italy G erm any Japan The Wealth-based Sustainability Indicator, (Università La Sapienza di Roma) Fiscal Sustainability December / 23

33 Empirical Results The path for Germany and Italy is sustainable, because the index converges to a value F 0. (Università La Sapienza di Roma) Fiscal Sustainability December / 23

34 Empirical Results The path for Germany and Italy is sustainable, because the index converges to a value F 0. The path for France and Japan is unsustainable, because the index systematically displays a value F > 0. (Università La Sapienza di Roma) Fiscal Sustainability December / 23

35 Empirical Results The path for Germany and Italy is sustainable, because the index converges to a value F 0. The path for France and Japan is unsustainable, because the index systematically displays a value F > 0. Comparing the previous with the following gures, showing the behavior of the government debt-wealth ratio, it emerges (b t /r) /W t > F > 0 for France and F > (b t /r) /W t for Japan. (Università La Sapienza di Roma) Fiscal Sustainability December / 23

36 Empirical Results France Italy G erm any Japan The Government Debt-Wealth Ratio, (Università La Sapienza di Roma) Fiscal Sustainability December / 23

37 Conclusions In the literature the sustainability of scal policy is periodically assessed on the basis of the debt-gdp ratio. (Università La Sapienza di Roma) Fiscal Sustainability December / 23

38 Conclusions In the literature the sustainability of scal policy is periodically assessed on the basis of the debt-gdp ratio. Inconsistency if one refers to dynamic macroeconomic theory, whereby forward-looking agents s optimization incorporates transversality conditions. (Università La Sapienza di Roma) Fiscal Sustainability December / 23

39 Conclusions In the literature the sustainability of scal policy is periodically assessed on the basis of the debt-gdp ratio. Inconsistency if one refers to dynamic macroeconomic theory, whereby forward-looking agents s optimization incorporates transversality conditions. We derive a a wealth-based sustainability index of government scal policy using a typical endogenous growth optimizing model. (Università La Sapienza di Roma) Fiscal Sustainability December / 23

40 Conclusions In the literature the sustainability of scal policy is periodically assessed on the basis of the debt-gdp ratio. Inconsistency if one refers to dynamic macroeconomic theory, whereby forward-looking agents s optimization incorporates transversality conditions. We derive a a wealth-based sustainability index of government scal policy using a typical endogenous growth optimizing model. Applying the index to post-1999 data, the scal stance is found to be sustainable for both Germany and Italy, weakly unsustainable for France, and strongly unsustainable for Japan. (Università La Sapienza di Roma) Fiscal Sustainability December / 23

41 Conclusions In the literature the sustainability of scal policy is periodically assessed on the basis of the debt-gdp ratio. Inconsistency if one refers to dynamic macroeconomic theory, whereby forward-looking agents s optimization incorporates transversality conditions. We derive a a wealth-based sustainability index of government scal policy using a typical endogenous growth optimizing model. Applying the index to post-1999 data, the scal stance is found to be sustainable for both Germany and Italy, weakly unsustainable for France, and strongly unsustainable for Japan. Fiscal rules of the type enshrined in the Fiscal Compact in the European Union are misleading. (Università La Sapienza di Roma) Fiscal Sustainability December / 23

42 Conclusions In the literature the sustainability of scal policy is periodically assessed on the basis of the debt-gdp ratio. Inconsistency if one refers to dynamic macroeconomic theory, whereby forward-looking agents s optimization incorporates transversality conditions. We derive a a wealth-based sustainability index of government scal policy using a typical endogenous growth optimizing model. Applying the index to post-1999 data, the scal stance is found to be sustainable for both Germany and Italy, weakly unsustainable for France, and strongly unsustainable for Japan. Fiscal rules of the type enshrined in the Fiscal Compact in the European Union are misleading. Indicators and tests of government solvency, used by the scal policy literature, are distorted because they exclude the debt-wealth ratio from the analysis. (Università La Sapienza di Roma) Fiscal Sustainability December / 23