Optimal Debt-Targeting Rules in a Small Open Economy∗ Huixin Bi† Bank of Canada January 7, 2011

Abstract

Optimal debt-targeting rules are studied in a real small open economy in which the government has to pay a debt-elastic sovereign risk premium. The debt-targeting rule sets the tax rate as a function of government indebtedness. The conventional random-walk tax smoothing outcome may no longer be optimal in this case, since the government faces a trade-off between smoothing the tax rate and stabilizing the sovereign interest rate. The optimal rule is found to be country specific and shock specific. Higher sovereign risk or shocks that have a larger impact on the government deficit call for the government to pursue more aggressive tax adjustments. In a model calibrated to a typical EMU country, the consumption tax is the most welfareimproving instrument, followed by the labor tax.

JEL Classification: E62; H63; F41 Keywords: Optimal fiscal policy, sovereign risk premium, small open economy ∗

I am grateful to Eric Leeper for inspiring my interest on this topic. I thank Eric Leeper, Troy Davig, Brian Peterson, and Todd Walker for many suggestions. The views expressed in this paper are those of the author and not of the Bank of Canada. † International Economic Analysis Department, Bank of Canada. 234 Wellington St., Ottawa, ON K1A 0G9, Canada. Email: [email protected].

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1 Introduction In the wake of the global financial crisis of 2007-2009, the skyrocketing interest rates on sovereign bonds in some small member countries of the European Economic and Monetary Union (EMU), such as Greece, Spain, Portugal, and Ireland, highlight the diminishing willingness of foreign investors to finance persistent government deficits. The spread between 10-year Greek government bonds and equivalent German bonds widened to more than 900 basis points in September 2010. More broadly, the large public debts accumulated in recent decades, coupled with the projection of an aging population, have raised severe fiscal challenges in many EMU countries. Fiscal adjustments are, or will be, inevitable in the attempts to fill the huge fiscal holes left by chronic government deficit and bold fiscal stimulus packages. When the government is unable or unwilling to cut government spending, taxes must be adjusted. Seminal work by Barro (1979), Lucas and Stokey (1983), and Aiyagari, Marcet, Sargent, and Seppala (2002) has shown that in a closed economy, taxes should be smoothed across time or over economic situation, and that government debt should be used as a shock absorber. Schmitt-Grohe and Uribe (2007), Kirsanova and Wren-Lewis (2007), and Kollmann (2008) extend the discussion by considering the optimal simple fiscal policy rule jointly with a monetary policy rule. They find that the optimal fiscal feedback should be small and that the tax-smoothing outcome still holds. However, it is still worthwhile to study the optimal debt-targeting rule in a small open economy for two reasons. First, the discussion has been largely limited to a closed economy. The policy implications may be different when the economy opens up, especially if the government has to pay a sovereign risk premium that depends on government indebtedness and if the economy is without an exchange rate instrument. The government may face a trade-off between smoothing the tax rate and stabilizing the sovereign interest rate. Second,

active tax policies can play an important role in stabilizing the economy when monetary policy cannot be used, as is the case for member countries of the EMU. A real business cycle model augmented by distorting taxes is used to analyze the optimal debt-targeting rules in a small open economy. Under a fixed global interest rate, the household can trade in the international financial market with some adjustment costs. The government issues non-state-contingent bonds in the international market and collects distorting tax revenue to finance exogenous and unproductive spending. The government also follows simple debt-targeting rules by adjusting the tax rates when the share of the government debt over GDP deviates from its steady-state level. The key feature of this model is that the government faces a sovereign risk premium that is positively dependent on government indebtedness. The heavier the government debt burden is, the higher sovereign interest rate the government has to pay. The positive correlation between the sovereign risk premium and government indebtedness is widely identified in empirical studies. Three findings emerge from the analysis. First, the conventional random-walk tax smoothing outcome may no longer be optimal in a small open economy. Under the debt-elastic sovereign interest rate, the government faces a trade-off between smoothing the tax rate and stabilizing the sovereign interest rate. Household welfare as a function of the tax-adjustment parameter features an inverted-U shape. Aggressive tax adjustments raise the volatility of the tax rate and the labor supply, reducing household welfare. Sluggish tax adjustments, on the other hand, retire the government debt more slowly, raising the volatility of the sovereign interest rate and the government deficit. In an economy that is without an exchange rate instrument – a reasonable assumption for EMU member countries – a more volatile government deficit may result in more volatile household consumption through the link of the trade deficit. Second, the optimal debt-targeting rule is country specific and shock specific. Higher sovereign risk or shocks that have a larger impact on the government deficit call for the

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government to pursue more aggressive tax adjustments. Third, a consumption tax is the most welfare-improving instrument, followed by a labor tax. The government should not use a capital tax to retire debt, if possible. Section 2 presents empirical evidence for the debt-elastic risk premium. Section 3 presents a simple model that contains only a labor tax to highlight that the debt-elastic sovereign interest rate may keep tax smoothing from being optimal. In Section 4, extended models containing consumption and capital taxes, in addition to a labor tax, are considered. The models are calibrated to a typical EMU economy in order to shed some light on the policy debate. Section 5 concludes.

2 Evidence on Government Debt and Risk Premia In this paper, sovereign risk premia increase in line with government indebtedness, providing a framework that is particularly relevant to recent policy debates regarding fiscal consolidation in some highly indebted EMU countries. Figure 1 plots the government debt-to-GDP ratios in EMU countries in 2010 against the yield spreads between 10-year government bonds in those countries and equivalent German bonds. It shows that, in general, a higher level of government debt raises the sovereign bond spread. This relationship between government debt and the sovereign interest rate is consistent with existing the empirical literature. Alesina, De Broeck, Prati, and Tabellini (1992) find a positive correlation between the size of public indebtedness and the sovereign risk premia in 12 OECD countries. The magnitude of the correlation, however, varies across countries: in a response to a 10% increase in the government debt-to-GDP ratio, the sovereign risk premium may rise by 10 basis points in some countries but by 1.7 percentage points in others, depending on the existing level of government debt. Lemmen and Goodhart (1999) show that an increase in the ratio of government debt to GDP has a positive and strongly significant impact on the sovereign interest spread in 13 countries of the EMU. By focusing on the EMU in the period 1993-2005, Bernoth, von Hagen, and Schuknecht (2006) find that 4

fiscal imbalances in most member countries raise their sovereign interest rate against that of Germany. A debt-to-GDP ratio that exceeds Germany’s by 10% causes a yield spread of around 7.7 percentage points. A recent study from the OECD by Haugh, Ollivaud, and Turner (2009) analyzes large movements in the yield spreads for sovereign bonds between Germany and other euro area countries in the period 2007-2009. They predict that an increase in the debt-service ratio of 3 percentage points can raise the spread, depending on risk aversion in the financial market and on the country’s fiscal track record, by an amount between 16 basis points to 1.49 percentage points. Garcia-Cicco, Pancrazi, and Uribe (2010) conduct Bayesian estimation of a real-business-cycle model augmented by a country-spread shock using Argentine and Mexican data for the period 1900-2005. They demonstrate that an increase in the external debt of 10% of GDP raises the sovereign risk premium by over 5 percentage points.

3 A Simple Model with Labor Tax In a real small open economy with linear production technology, the real output (yt ) is

yt = At Lt

(1)

where Lt denotes the labor supply and At the productivity level. Household: A representative household can purchase a risk-free foreign bond at the global interest rate (R). This model suffers from the well-known non-stationary problem because of the exogenous interest rate. Following Schmitt-Grohe and Uribe (2003b), the household is assumed to face a quadratic cost of holding bonds in quantities different from the steadystate level, given by ψb (bt − b)2 /2, which is zero at the steady state. The household pays a proportional tax (τtL ) on labor income and chooses consumption (ct ) and working hours (Lt )

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according to max E0

∞ X

β t u (ct , Lt )

(2)

t=0

s.t. ct + bt +


ψb (bt − b)2 = At Lt 1 − τtL + Rbt−1 . 2

(3)

The first-order conditions show that the labor tax rate introduces a wedge between the real wage and the marginal rate of substitution between consumption and leisure, see Equation 4, and that the marginal benefit of holding an additional unit of bonds equates to its marginal cost, see Equation 5. uL (t) = At (1 − τtL ) uc (t) uc (t + 1) 1 + ψb (bt − b) βEt = . uc (t) R −

(4) (5)

Government: The government finances exogenous spending (gt ) by taxing labor income and issuing non-state-contingent bond (dt ) in the international market. The key feature of this model, as discussed in Section 2, is that the interest rate on sovereign debt (Rtd ) increases with respect to government indebtedness.

d dt + At τtL Lt = Rt−1 dt−1 + gt

Rtd = R exp φ sdt−1 − sd

(6)



(7)

Equation 7 depicts the positive relationship between the interest rate and the ratio of government debt to GDP (sdt ), which is similar to the specifications in Garcia-Cicco, Pancrazi, and Uribe (2010) and Corsetti, Kuester, Meier, and Muller (2010). The parameter φ measures country-specific sovereign risk: for a given debt-to-GDP ratio, a larger φ leads to a higher risk premium. sdt is defined as dt /yt , with sd representing the steady-state level. In addition, the government pursues an explicit debt target (sd ) using the instrument of the labor tax. The parameter γ L measures the government’s willingness to retire debt by

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raising the tax: a larger γ L implies more aggressive tax adjustments.

ln

sdt−1 τtL L = γ ln τL sd

(γ L > 0)

(8)

Transversality condition: In a closed economy, the transversality condition of a household’s asset holding prohibits the government from running a Ponzi scheme. In an open economy, however, Benigno (2005) shows that the no-Ponzi-game constraint on the household does not guarantee that the government will not run a Ponzi scheme against the rest of the world. This study follows Schmitt-Grohe and Uribe (2003a) by assuming that before the government can borrow from the international market, it must satisfy the following constraint

j=i−1

lim Et

i→∞

Y j=0

1 dt+i = 0. d Rt+j

(9)

Shocks: The shocks to government spending and productivity follow AR(1) processes. gt gt−1 = ρg log + εgt g g At A t−1 log = ρA log + εA t A A log

εgt ∼ N (0, σg2) 2 εA t ∼ N (0, σA ),

(10) (11)

where g and A denote the steady-state levels of government spending and productivity. 3.1 Method and Benchmark Calibration

In the absence of a closed-form solu-

tion, the equilibrium conditions are approximated around the deterministic steady state. A second-order solution is necessary, since the conventional linearization can generate spurious welfare reversals, see Kim and Kim (2003). The perturbation method presented by SchmittGrohe and Uribe (2004) is used to perform a full second-order approximation of the model and to numerically optimize the tax-adjustment parameter by way of grid searches. If V0a denotes the conditional welfare associated with a debt-targeting rule a, then λa is the welfare cost of adopting rule a on the condition of the calibrated steady state. Let the optimal

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debt-targeting rule (opt) be the reference case, then λa − λopt is the fraction of consumption that a household would be willing to tolerate while remaining indifferent between the rule a and the optimal rule opt.

V0i

≡ E0 = E0

∞ X t=0 ∞ X

β t U(cit , Lit )

(i = a, opt)

β t U((1 − λi )c, L)

t=0

We assume the utility function is cχ (1 − L)1−χ U(c, L) = 1−σ


1−σ

.

(12)

The inverse of the intertemporal elasticity of consumption (σ) is set to 2, which is standard in business-cycle studies. The parameter χ is calibrated to ensure that the Frisch elasticity is 3 and that the household spends 25% of its time working. The discount factor is 0.95 and, therefore, the global interest rate is 1.05. The bond-adjustment cost parameter (ψb ) is 0.02, which implies that a change in household bond holdings of 10% of GDP costs only 0.00315% of household consumption.1 All the fiscal variables are calibrated to European data, as explained in Appendix A. Government spending is calibrated to 20% of GDP and household consumption is 80 percent of GDP. In the benchmark case, the government debt is 57% of GDP and the labor tax is 0.23. The sovereign risk parameter is 0.1, implying that an increase in the government debt of 10% of GDP raises the sovereign interest rate by 1.05 percentage points, which is within the range of empirical estimations. In addition, the shocks to productivity and government spending have a persistence of 0.62 and a standard deviation of 0.02. 1

All welfare comparisons in this paper are robust to alternative calibrations for ψb as far as it is sufficiently large to ensure that the model is stationary, see Schmitt-Grohe and Uribe (2003b).

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3.2 Numerical Result

This simple model is used to analyze household welfare by

performing a one-dimension grid search over the tax-adjustment parameter. All the welfare curves are plotted against their own optimal level, λa − λopt , with the optimal welfare level (λopt ) being normalized to zero. 3.2.1 Benchmark Case

The benchmark case focuses on the shock to government spend-

ing by fixing productivity at its steady-state level. The top panel of Figure 2 shows that the welfare curve, featuring an inverted-U shape, peaks when the tax-adjustment parameter (γ L ) reaches 0.82. The numerical value of γ L can be better understood through the linearization of the debt-targeting rule, Equation 8, around the steady state. ∆τtL ≈

γ Lτ d ∆st sd

(13)

By setting γ L to the optimal value of 0.82, the government would, under the benchmark calibration, raise the tax rate by 3.3 percentage points for a marginal increase in government debt of 10% of GDP. If the government deviates from the optimal rule, the household may suffer a substantial welfare loss. For instance, if the government sets γ L to 0.35, raising the tax rate by only 1.6 percentage points for a marginal increase in government debt of 10% of GDP, the household would be worse off by 6.7 percent of its consumption. On the other hand, if the government sets γ L to 1.6, raising the tax rate by 6.6 percentage points for the same marginal increase in government debt, the household would be worse off by 6.14 percent of its consumption. The middle and bottom panels of Figure 2 explain why neither sluggish nor aggressive tax adjustments improve the household’s welfare. In this small open economy, the government faces a trade-off between smoothing the tax rate and stabilizing the sovereign interest rate. Aggressive tax adjustments raise the volatility of the tax rate and the labor supply, leading to more volatile household consumption and lower welfare. Sluggish tax adjustments, on the other hand, lower the volatility of the tax rate and the labor supply, but they raise the 9

volatility of the sovereign interest rate by retiring the government debt more slowly. The latter would be channeled into higher volatility of the government deficit. In an economy that is lacking an exchange rate instrument – a reasonable assumption for EMU member countries – a more volatile government deficit may translate into more volatile household consumption through the link of the trade deficit. The positive correlation between the “twin deficits” plays a key role in generating the inverted-U-shaped welfare curve.  
ψb 2 d At Lt − ct + gt + (bt − b) = (bt − Rbt−1 ) − dt − Rt−1 dt−1 2

(14)

3.2.2 Closed Economy versus Open Economy In this section, the benchmark model is compared with an otherwise identical closed economy. The household and the government are constrained by Equations 15 and 16, respectively. The interest rate on government bonds, endogenously determined in the domestic bond market, no longer depends on the countryspecific sovereign risk. As the bond market clears, the aggregate economy is subjected to the constraint in Equation 17. The government still follows the same debt-targeting rule as in the open economy, specified in Equation 8.


b ct + bt = At Lt 1 − τtL + Rt−1 bt−1

(15)

ct + gt = At Lt

(17)

b bt + τtL At Lt = Rt−1 bt−1 + gt

(16)

The top left panel of Figure 3 shows that each economy requires a different optimal debttargeting rule. When the government pursues more aggressive tax adjustments, household welfare decreases monotonically in the closed economy but follows an inverted-U shape in the open economy. The observation that slower tax adjustments always improve welfare in the closed economy is consistent with the existing literature: Barro (1979) and Aiyagari, Marcet, Sargent, and Seppala (2002) show that under Ramsey optimal fiscal policy, government debt

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should be a shock absorber and distorting tax should follow a random walk. In this closed economy, the smaller the tax-adjustment parameter becomes, the closer the tax process gets to a random walk. In the open economy, however, the government faces the debt-elastic sovereign risk premium, from which emerges the trade-off between smoothing the tax rate and stabilizing the sovereign interest rate. In addition, when the government deviates from the optimal debt-targeting rule, the welfare cost is much larger in the open economy than in the closed economy. When the tax-adjustment parameter increases from 0.4 to 1.6, household welfare deteriorates by only 0.25% of its consumption in the closed economy but by 5% in the open economy. 3.2.3 Different Shocks

The bottom left panel of Figure 3 compares household wel-

fare under the productivity shock and under the government spending shock, with both shock processes featuring the same persistence and variance. Under the productivity shock, household welfare peaks when the tax-adjustment parameter reaches to 0.46, which falls into the lower end of its feasible range. Deviations from this optimal rule may reduce household welfare by less than 0.7% of its consumption. In contrast, the government spending shock calls for the government to pursue much more aggressive tax adjustments. Failing to do so can reduce household welfare by as much as 5% of its consumption. This contrast arises from the different impacts of the two shock on the government deficit. As explained in Section 3.2.1, sluggish tax adjustments may raise the volatility of the sovereign interest rate and, therefore, that of the government deficit, which is channeled into more volatile trade deficit and household consumption. The spill-over effect to the government deficit from the government spending shock is much stronger than that from the productivity shock, since the former affects the government deficit directly, while the latter can affect the deficit only through tax revenue. For the same persistence and variance, the productivity shock generates less volatility in the government deficit than the government spending shock.

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3.2.4 Different Levels of Sovereign Risk

The elasticity of the sovereign risk

premium with respect to government indebtedness depends on the sovereign risk parameter (φ). Linearization of the debt-elastic interest rate around the steady state, given by Equation 18, implies that increasing government debt by 1% of GDP raises the sovereign interest rate by about 1.05φ percentage points.

∆Rtd ≈ Rφ∆sdt−1

(18)

The top right panel of Figure 3 compares household welfare under different levels of sovereign risk: the dashed line illustrates household welfare with low sovereign risk (φ = 0.05), the solid line shows the benchmark case (φ = 0.1), and the dash-dotted line illustrates high sovereign risk (φ = 0.2). These three calibrations of sovereign risk imply that an increase in government debt of 10% of GDP may raise the sovereign interest rate by 52.5 basis points, 1.05 percentage points, and 2.1 percentage points, respectively, all of which fall within the range of empirical estimations. The comparison shows that higher sovereign risk calls for more aggressive tax adjustments. As sovereign risk increases from 0.05 to 0.2, the optimal tax-adjustment parameter should rise from 0.63 to 1.07. It implies that to maximize household welfare, the government should raise the tax rate by 4.4 percentage points instead of 2.5 percentage points when responding to an increase in its debt of 10% of GDP, because higher sovereign risk intensifies the spill-over from government spending to household consumption through the “twin deficits.” Higher sovereign risk also raises the welfare cost of deviating from the optimal rule. The higher the sovereign risk, the steeper the welfare curve becomes. When the sovereign risk is low (φ = 0.05), welfare falls by 3% of consumption as the tax-adjustment parameter deviates from the optimal point by ±0.5. If the risk is high (φ = 0.2), on the other hand, welfare falls by 6% of consumption.

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The bottom right panel of Figure 3

3.2.5 Different Level of Government Debt

compares household welfare under different levels of government debt. Steady-state government debt is calibrated to 57% of GDP for the solid line, 38% for the dashed line, and 76% for the dash-dotted line. The comparison shows that the heavier the debt burden, the faster the tax adjustment should be. As government debt increases from 38% of GDP to 76% at the steady state, the optimal tax-adjustment parameter should increase from 0.61 to 0.98, which implies that the government should raise the tax rate by 4 percentage points instead of 2.5 percentage points for a marginal increase in government debt of 10% of GDP. In addition, a smaller debt burden flattens the welfare curve, implying a smaller welfare cost when the government deviates from the optimal rule.

4 Optimal Choice of Tax Instrument This section extends the simple model in Section 3 by incorporating capital and consumption taxes to discuss the optimal choice of tax instrument. 4.1 Model with Labor and Capital Taxes

In the extended model, the household

can accumulate physical capital (kt ) by paying a quadratic adjustment cost that depends on the changes in the level of capital, given by φk (kt − kt−1 )2 /2. The assumption of the capital adjustment cost, the level and slope of which is zero at the steady state, is widely used in small-open-economy models to avoid excessive investment volatility. The household receives a wage for labor supply (wt ) and a return on capital (Rtk ), but also pays a labor tax (τtL ) and a capital tax (τtk ). Following Mendoza, Razin, and Tesar (1994), the capital tax is levied on the net-of-depreciation dividend, with δ being the capital depreciation rate. In addition, the household can still purchase foreign bonds at the global interest rate but incurs a quadratic

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adjustment cost.

max

E0

∞ X

β t u (ct , Lt )

(19)

t=0

s.t.

ct + kt + bt =



1 − τtL wt Lt + 1 − τtk (Rtk − δ)kt−1 + kt−1

−

φk φb (kt − kt−1 )2 + Rbt−1 − (bt − b)2 2 2

The optimization condition for capital stock, Equation 20, equates the marginal cost of investing one unit of consumption in capital today to the expected after-tax return in the next period.

1 = βEt

k k )(Rt+1 − δ) + 1 + φk (kt+1 − kt ) uc (t + 1) (1 − τt+1 . uc (t) 1 + φk (kt − kt−1 )

(20)

Taking the labor wage and the price of renting capital as given, the representative firm maximizes its profits subject to a production technology given by f (kt−1 , Lt ). max f (kt−1 , Lt ) − Rtk kt−1 − wt Lt .

(21)

The maximization conditions are

Rtk = fk (kt−1 , Lt )

(22)

wt = fL (kt−1 , Lt ) .

(23)

The government finances exogenous spending by issuing non-state-contingent bonds and collecting taxes on labor and capital income. The government also follows debt-targeting rules, through which the taxes on labor and capital are adjusted to target the government debt-to-GDP ratio at the steady-state level. The tax-adjustment parameters (γ L , γ k ) could be different from each other. The rest of the world purchases government bonds at the

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debt-elastic interest rate (Rtd ). d Rt−1 dt−1 + gt + z = dt + τtk (Rtk − δ)kt−1 + τtL wt Lt

sdt−1 τtL L = γ ln τL sd d k s τ ln tk = γ k ln t−1 τ sd

ln

Rtd = R exp φ sdt−1 − sd

4.1.1 Calibration

(24) (25) (26)





(27)

As elaborated in Appendix A, the model is calibrated to the EMU

data for the period 1971-2007. In the steady state, the capital tax rate is set to 0.19, the labor tax to 0.31, government spending to 21% of GDP, government debt to 62% of GDP, and household consumption to 64% of GDP. The production function is assumed to be

f (k, L) = Ak α L1−α .

(28)

Following Schmitt-Grohe and Uribe (2003b), the capital ratio (α) is calibrated to 0.32, the capital depreciation rate to 0.1, and the capital-adjustment parameter (φk ) to 0.028. A full second-order approximation of the model is performed and the tax-adjustment parameters are numerically optimized by way of two-dimension grid searches. All the welfare curves are plotted against their own optimal level, λa − λopt , with the optimal welfare normalized to zero. 4.1.2 Numerical Result

Figure 4 shows the welfare contour lines over γ L and γ k ,

the adjustment parameters on labor and capital taxes, with the welfare cost labeled on the corresponding contour line. The density of the contour lines measures the slope of the welfare surface, with more clustered lines implying a steeper welfare surface. The key message is that the government should use a labor tax, rather than a capital tax, to retire its debt, since household welfare peaks when the adjustment parameter on the labor tax is 0.7 and that on the capital tax is zero. This is because that the household can trade 15

foreign assets, but not labor supply, in the international market. Even a small change in the capital tax may motivate the household to substitute domestic physical capital for risk-free international bonds, generating sizeable swings in the capital stock and raising the volatility of the output and household consumption. On the other hand, if the government uses the labor tax to retire its debt, the trade-off between smoothing the tax rate and stabilizing the sovereign interest rate still exists and, therefore, the inverted-U-shaped welfare curve is preserved. Compared with the simple model, a deviation from the optimal debt-targeting rule has a much smaller impact on household welfare when the household can accumulate capital. When the labor-tax-adjustment parameter increases from the optimal point by 0.5, welfare falls by 0.046% of consumption, as shown in Figure 4, but by 1.93% of consumption in the absence of capital, as shown in Figure 2. The availability of capital provides an additional instrument with which the household can smooth its consumption. 4.2 Model with Taxes on Consumption, Capital and Labor

Along with taxes

on labor and capital, the government also collects a tax on household consumption (τtc ) in this model. In addition, the household is assumed to receive lump-sum transfers (z) from the government to match the data. The household budget constraint becomes

(1 + τtc )ct + kt + bt =



1 − τtL wt Lt + 1 − τtk (Rtk − δ)kt−1 + kt−1

−

φk φb (kt − kt−1 )2 + Rbt−1 − (bt − b)2 + z. 2 2

16

(29)

Letting ηt denote the Lagrange multiplier on the household budget constraint, the first-order conditions are

ηt =

uc (t) 1 + τtc

(30)

−uL (t) = ηt wt (1 − τtL )

(31)

1 ηt+1 1 = βEt R ηt 1 + φb (bt − b) k k )(Rt+1 − δ) + 1 + φk (kt+1 − kt ) ηt+1 (1 − τt+1 1 = βEt . ηt 1 + φk (kt − kt−1 )

(32) (33)

The government collects taxes on household consumption, labor, and capital income, and also follows the debt-targeting rules, through which the taxes are adjusted to target the debtto-GDP ratio at the steady-state level. The tax-adjustment parameters (γ c , γ L , γ k ) could be different from each other.

d Rt−1 dt−1 + gt + z = dt + τtk (Rtk − δ)kt−1 + τtL wt Lt + τtc ct

(34)

sdt−1 sd

(35)

ln

τtc τc

= γ c ln

sdt−1 τtL L = γ ln τL sd d k s τ ln tk = γ k ln t−1 τ sd

ln

(36) (37)

4.3 Numerical Result Table 1 shows that all fiscal variables are calibrated to the data, implying that the lump-sum transfers are 17% of GDP, the consumption tax is 0.19, the labor tax is 0.32, and the capital tax is 0.19. Government spending is set at 18% of GDP and the government debt is 55% of GDP at the steady state. The tax-adjustment parameters are numerically optimized by way of three-dimension grid searches. Figure 5 indicates that the government should use a consumption tax, rather than labor or capital taxes, to retire its debt, since household welfare peaks when the adjustment parameter on the consumption tax is 4.35 and those on labor and capital taxes are zero.

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The top left panel of Figure 5 shows the contour lines over γ c and γ L , the adjustment parameters on consumption and labor taxes, while the adjustment parameter on the capital tax is fixed at its optimal value of zero. Household welfare is hump-shaped over γ c , but decrease monotonically over γ L . The bottom left panel of Figure 5 shows the welfare lines over γ k and γ L , when γ c is kept at its optimal value of 4.35. Household welfare decreases monotonically over both γ k and γ L . Finally, the top right panel of Figure 5 shows the welfare lines over γ c and γ k , when γ L is fixed t its optimal value of zero. Again, household welfare is hump-shaped over γ c but decreases over γ k . Compared with the models without a consumption tax, a deviation from the optimal debt-targeting rule has an even smaller impact on household welfare when the government has the instrument of a consumption tax. For instance, Figure 5 shows that while the adjustment parameters on capital and consumption taxes are kept at their optimum, an increase of labor tax adjustment from its optimal point by 0.5 reduces household welfare by 0.0114 percent of consumption, which is 1/4 of that in the model with both capital and labor taxes and only 1/170 of that in the model with only a labor tax. In contrast to labor and capital taxes, which may provide strong incentives for the household to work or invest less, a consumption tax is less distorting since it can stabilize the government budget without destabilizing the economy. In addition, private consumption is close to 70% of aggregate output, which is about the same as the labor tax base and much larger than the capital tax base.

5 Conclusion This paper analyzes optimal debt-targeting rules in a small open economy, assuming that the government has to pay a sovereign risk premium that is positively dependent on its indebtedness, and that the economy has no exchange rate instrument. Both assumptions are made with a highly indebted EMU country in mind. In this case, the random-walk tax smoothing may no longer be optimal, since the govern18

ment faces a trade-off between smoothing the tax rate and stabilizing the sovereign interest rate. Slow tax adjustments can raise the volatility of the “twin deficits” and, therefore, that of household consumption. The optimal debt-targeting rule is country specific and shock specific. The consumption tax is found to be the most welfare-improving instrument, followed by the labor tax. Incorporating an endogenous sovereign risk premia may provide an interesting extension. Bi (2010) shows that a stochastic fiscal limit may endogenously arise from the dynamic Laffer curves, implied by distorting taxes.

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References Aiyagari, S. R., A. Marcet, T. J. Sargent, and J. Seppala (2002): “Optimal Taxation without State-Contingent Debt,” Journal of Political Economy, 110, 1220–1254. Alesina, A., M. De Broeck, A. Prati, and G. Tabellini (1992): “Default Risk on Government Debt in OECD Countries,” Economic Policy, 7(15), 428–463. Barro, R. J. (1979): “On the Determination of the Public Debt,” Journal of Political Economy, 87, 940–971. Benigno, P. (2005): Comment on “Fiscal Externalities and Optimal Taxation in an Economic Communit” by Marianne Baxter and Robert G. King, NBER International Seminar on Macroeconomics. MIT Press. Bernoth, K., J. von Hagen, and L. Schuknecht (2006): “Sovereign Risk Premiums in the European Government Bond Market,” GESY Discussion Paper No. 151. Bi, H. (2010): “Sovereign Default Risk Premia, Fiscal Limits and Fiscal Policy,” Manuscript, Indiana University. Corsetti, G., K. Kuester, A. Meier, and G. Muller (2010): “Fiming Fiscal Retrenchment in the Wake of Deep Recessions,” Manuscript, Presented at the 11th Jacques Polak Annual Research Conferece. Garcia-Cicco, J., R. Pancrazi, and M. Uribe (2010): “Real Business Cycle in Emerging Countries?,” American Economic Review, forthcoming. Haugh, D., P. Ollivaud, and D. Turner (2009): “What Drives Sovereign Risk Premiums? An Analysis of Recent Evidence from the Euro Area,” OECD Economics Department Working Papers, No. 718.

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Heston, A., R. Summers, and B. Aten (2009): “Penn World Table Version 6.3,” Center for International Comparisons of Production, University of Pennsylvania. Kim, J., and S. H. Kim (2003): “Spurious Welfare Reversals in International Business Cycle Models,” Journal of International Economics, 60, 471–500. Kirsanova, T., and S. Wren-Lewis (2007): “Optimal Fiscal Feedback on Debt in an Economy with Nominal Rigidities,” Federal Reserve Bank of Atlanta Working Paper, 2007-26. Kollmann, R. (2008): “Welfare-Maximizing Operational Monetary and Tax Policy Rules,” Macroeconomic Dynamic, 12, 112–125. Lemmen, J. J., and C. A. Goodhart (1999): “Credit Risks and European Government Bond Markets: A Panel Data Econometric Analysis,” Eastern Economic Journal, 25, 77–107. Lucas, R. E. J., and N. L. Stokey (1983): “Optimal Fiscal and Monetary Policy in an Economy without Capital,” Journal of Monetary Economics, 12, 55–93. McDaniel, C. (2007): “Average Tax Rates on Consumption, Investment, Labor and Capital in the OECD 1950-2003,” Manuscript, Arizona State University. Mendoza, E. G., A. Razin, and L. L. Tesar (1994): “Effective Tax Rates in Macroeconomics Cross-country Estimates of Tax Rates on Factor Incomes and Consumption,” Journal of Monetary Economics, 34, 297–323. Schmitt-Grohe, S., and M. Uribe (2003a): “Anticipated Ramsey Reforms and the Uniform Taxation Principle: The Role of International Financial Markets,” European Central Bank Working Paper, 210. (2003b): “Closing small open economy models,” Journal of International Economics, 61, 163–185. 21

(2004): “Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function,” Journal of Economic Dynamics and Control, 28, 755–775. (2007): “Optimal Simple and Implementable Monetary and Fiscal Rules,” Journal of Monetary Economics, 54, 1702–1725.

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A Data Appendix Other than tax rates, all the fiscal variables are calibrated to the average of the following European countries for the period between 1970 and 2007: Austria, Belgium, Finland, France, Greece, Ireland, Italy, Netherlands, and Spain. The data on government spending and lump-sum transfers are from the OECD Economic Outlook No. 84 (2009): total government spending includes government consumption of fixed capital and government final consumption expenditures, while the lump-sum transfers are defined as the sum of social security payments, net capital transfers and subsidies. The data on gross debt, which is defined as all financial liabilities of general government, are taken from the European Commission Economic database (Autumn 2009). Owing to data limitation, labor, consumption and capital tax rates are calibrated to a smaller set of countries for the period 1970-2003: Austria, Belgium, Finland, France, Germany, Italy, Netherlands, and Spain. The database was complied by McDaniel (2007). Using a Hodrick-Prescott filter, we detrend the data for the real GDP per worker from Penn World Table Version 6.3 (see Heston, Summers, and Aten (2009)) and estimate the shock process of productivity. Table 1: Calibration Variable Data Simple Model g/y 0.21 0.2 d/y 0.58 0.57 τL 0.32 0.23 k τ 0.19 n.a. τc 0.19 n.a. z/y 0.17 n.a.

Model with τ L and τ k 0.21 0.62 0.31 0.19 n.a. n.a.

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Model with τ c , τ L and τ k 0.18 0.55 0.32 0.19 0.19 0.17

10−year government bond spread against Germany (Percentage point)

10

8

6

4

2

0 20

40

60 80 100 120 General government gross debt−to−GDP ratio (2010)

140

Figure 1: Yield spreads on 10-year government bonds (against German bond) versus the general government gross debt in 2010 in EMU countries. Source: ECB and IMF (Global Financial Stability Report, October 2010).

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Welfare (λa−λopt) ∆ c/c (in percentage)

2 0 −2 −4 −6 −8 0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

L

Tax adjustment parameter (γ ) Variances of tax rate and interest rate 0.1

0.01 0.008 measured on the left axis

measured on the right axis 0.06

0.006

0.04

0.004

0.02

0.002

0 0.2

0.4

0.6

0.8

1

1.2

1.4

Var(R)

Var(τL)

0.08

0 1.6

Tax adjustment parameter (γL) Variances of consumption and labor supply 0.0016

0.03

0.0014

0.025

0.0012

0.02 measured on the left axis

0.001

0.015

0.0008

0.01

0.0006

0.005

0.0004 0.2

0.4

0.6

0.8

1

1.2

1.4

Var(L)

Var(c)

measured on the right axis

0 1.6

L

Tax adjustment parameter (γ )

Figure 2: Welfare and variance comparisons in the simple model with only a government spending shock. The optimal welfare λopt is normalized to zero.

25

Closed vs. Open Economy

Different Sovereign Risk 1

−0.1

−2

−1

Open

Closed

0

measured on 0 the right axis

0

−2 −3 −4

−0.2

measured on the left axis

−4

Small φ Benchmark Large φ

−5 −6

−0.3

0.5

1

1.5

−6

−7

0

0.5

L

Different Debt−GDP 1 0

−0.2

−1

−0.4

−2

−0.6

−3 measured on the right axis 1

−4 1.5

−5

Government purchase shock

Productivity shock

Different Shocks

0.5

2

γ

0.2 measured on the left axis 0

−1

1.5

L

γ

−0.8

1

γL

0 −2 −4 −6 Low d/y Benchmark High d/y

−8 −10

0

0.5

1

1.5

2

γL

Figure 3: Welfare comparisons in the model with only labor tax. The optimal welfare λopt is normalized to zero.

26

a

opt

Welfare (λ −λ

)

k

−0.12 −0.1

−0.08

−0.06

−0.04

−0.02

0.35

−0.02

−0.16 −0.14

0.3 0.25

−0.12 −0.1

−0.08

−0.06

−0.04

−0.02

0.2

−0.02

−0.14

0.15 0.1

1.2

−0.12 −0.1

1

−0.08

0.8

−0.06

0.6

−0.04

0

−0.02

0.05

−0.02

Adjustment parameter on capital tax (γ )

0.4

1.4 L

Adjustment parameter on labor tax (γ )

Figure 4: Welfare contour plot in the model with both labor and capital taxes.

27

Adjustment parameter on consumption tax (γc)

c

6 5.5

4

−0.011 −0.009

−0.00

5

06 −0.0 05 −0.0

4.5 .00 1

4

−0

3.5

2.5 2 0

0.1

0.2

0.3

.0

3

12

02 .0 −0 03 .0 −0 8 6 007 .00 0.01 4 05 − −0.00 −0.0 −0.00 −0. −0

13 .0

−0

Adjustment parameter on consumption tax (γ )

Welfare (λa−λopt)

−0

0.4

0.5 L

6 5.5 5 4.5 4 3.5

−0.001

3 2.5 2 0

0.1

0.2

−0.002 −0.003 −0.004 −0.005 0.3

0.4 k

Adjustment parameter on labor tax (γ )

Adjustment parameter on capital tax (γ )

Welfare (λa−λopt) 0.4 0.35 −0.013

0.3 0.25

−0.005

−0.004

−0.003

0.1

−0.002

0.15

−0.012−0.011 −0.01 −0.009 −0.008 −0.007 −0.006

0.2 −0.001

Adjustment parameter on capital tax (γk)

Welfare (λa−λopt)

0.05 0

0

0.1

0.2

0.3

0.4

0.5 L

Adjustment parameter on labor tax (γ )

Figure 5: Sliced welfare contour plots in the model with taxes on consumption, labor and capital income. The maximum welfare, obtained at γ c = 4.35 and γ L = γ k = 0, is normalized to zero. Top left panel: γ k is kept at zero; bottom left panel: γ c is kept at the optimum; top right panel: γ L is kept at zero.

28