Chapter 5 Fiscal Policy and Economic Growth · depreciation, have a negative impact on savings and investment. Such taxes affect savings and capital accumulation negatively, and,

George Alogoskoufis, Dynamic Macroeconomic Theory, 2015

Chapter 5 Fiscal Policy and Economic Growth

In this chapter we introduce the government into the exogenous growth models we have analyzed so far. We first introduce and discuss the inter-temporal budget constraint of the government and the conditions for government debt sustainability. Then, we analyze the impact of the level of lump sum taxes, primary government expenditure and government debt in the representative household model and a model of overlapping generations. Finally, we analyze the short and long term effects of distortionary taxes on labor and capital income, consumption and business profits before interest and depreciation.

The government budget constraint is defined in a way which is similar to the inter-temporal budget constraint of a household that can borrow and lend freely at the market interest rate. It requires the equality of the present value of current and future tax revenue to the sum of the current stock of government debt and the present value of current and future primary government expenditure. Primary government expenditure is defined as government expenditure excluding interest payments on government debt, and present values are calculated using the market interest rate.

The budget constraint of a government with an infinite horizon does not prevent it from having debt, or even from increasing the level of its debt. It means, however, that the limit of the present value of government debt, as time tends to infinity, cannot be positive. For example, if the real interest rate is positive, a positive but constant real government debt - which means that the government never repays it - satisfies the government budget constraint. Even if government debt increases continuously, the government budget constraint is satisfied to the extent that the real interest rate exceeds the growth rate of real government debt.

When one introduces the government budget constraint in the representative household model, it can be shown that the only aspect of it that matters for the choice of the optimal path of private consumption, is the present value of primary government expenditure. The method of financing primary government expenditure, i.e the breakup between government debt and (non-distortionary) taxes, does not affect the optimal path of consumption of the representative household. This property is known as Ricardian equivalence between taxes and government debt. In other words, the stock of government bonds held by the representative household is not considered as part of its total wealth, and does not affect its consumption path. The representative household realizes that the bonds will be financed by future taxes equal in present value to the stock of existing government debt.

Ricardian equivalence does not apply to overlapping generations models. The stock of government debt affects aggregate savings, as current generations realize that part of the present value of future taxes required to finance the stock of government debt, will be paid by future generations. In overlapping generations models, current generations are not concerned with the welfare of future

George Alogoskoufis, Dynamic Macroeconomics, 2015 Chapter 5

generations. Thus, current generations treat part of the existing stock of government debt that they hold as part of their wealth, since it exceeds the present value of their own future taxes. As a result, debt and tax finance are not equivalent in overlapping generations models, and Ricardian equivalence does not hold.

Therefore, in overlapping generations models, both the stock of real government debt and real primary government expenditure affect private and total savings, and the accumulation of capital. Rises in real government debt or real primary government expenditure reduce savings and capital accumulation, and have negative effects on the steady state capital stock, output, private consumption and real wages. This is because current generations know that part of the increase in future tax revenues in order to finance a higher level of primary government expenditure and/or interest payments on the increased debt, will be shouldered by future generations. Private savings are thus affected negatively by an increase in real government debt, and total savings, private and government, are affected negatively by an increase in real primary government expenditure. This leads to an adjustment process with a declining capital stock and private consumption, and a lower steady state level of capital, output and consumption per head.

Taxes are rarely non-distortionary, as they affect incentives for savings, investment and labor supply. In the representative household and overlapping generations models that we have considered, labor supply is exogenously given, and does not depend on net of tax real wages. Consequently, tax rates on labor income or (time invariant) consumption taxes do not cause distortions in labour supply and savings, and do not affect either the adjustment path or the balanced growth path. In contrast, capital income taxation and taxes on business earnings before interest and depreciation, have a negative impact on savings and investment. Such taxes affect savings and capital accumulation negatively, and, as a result, have a negative impact on the steady state capital stock, steady state output and income, steady state real wages and steady state private consumption.

5.1 The Government Budget Constraint

For a household that can borrow and lend freely at a market determined interest rate, the inter-temporal budget constraint requires that the present value of its current and future consumption cannot exceed the value of its current assets, plus the present value of its future labor income (see Chapter 2). The inter-temporal budget constraint of a government that can borrow and lend freely at a market determined interest rate is defined accordingly: The present value of its current and future primary government expenditure cannot exceed the value of its current assets, plus the present value of its current and future tax receipts.

5.1.1 Primary Government Expenditure, Taxes and Government Debt

The inter temporal government budget constraint can be written as,

! (5.1)

where,

!

r(s) the real interest rate at time s

e−R(t )Cg (t)dt ≤ −D(0) + e−R(t )T (t)dtt=0

∞

∫t=0

∞

∫

R(t) = r(s)dss=0

t

∫

!2


Cg(t) real government purchases of goods and services at time t T(t) real tax revenue at time t D(0) real government debt at time 0

Cg, the value of real government purchases of goods and services, is often referred to as real primary government expenditure.

As in the case of the representative household model in Chapter 2, we can define the average real interest rate between time 0 and time t as,

!

With this definition, (5.1) can also be written as,

! (5.1΄)

The government budget constraint does not stop the government from having debt continuously, or even from increasing the stock of its debt. However, the present value of future government debt as time goes to infinity cannot possibly be positive. As for households, this implies a transversality condition of the form,

! (5.2)

For example, if the real interest rate is positive, a positive constant stock of real government debt - something which means that the government never pays it back - satisfies the government budget constraint. Even if the stock of real government debt is increasing over time, the budget constraint of the government and the transversality condition (5.2) are satisfied, as long as the growth rate of real government debt does not exceed the average real interest rate.

5.1.2 Overall and Primary Government Deficits

The simplest definition of the overall government deficit (or simply government deficit) is that this is equal to the difference between total government expenditure and total government revenue. The government deficit determines the change in the stock of government debt.

Taking the first derivative of the government budget constraint with respect to time, the total government deficit is defined as,

! (5.3)

The term in brackets in the right hand side of (5.3) is called the primary deficit. Thus, the total government deficit is the primary deficit plus interest payments on government debt.

r_(t) = 1

tr(s)ds = 1

tR(t)

s=0

t

∫

e− r_(t )tCg (t)dt ≤ −D(0)+ e− r

_(t )tT (t)dt

t=0

∞

∫t=0

∞

∫

limt→∞

e−R(t )D(t) = limt→∞

e− r_(t )tD(t) ≤ 0

D•(t) = [Cg (t) − T (t)]+ r(t)D(t)

!3


The primary deficit is a very informative index of the contribution of fiscal policy to the evolution of government debt. For example, we can write the inter-temporal government budget constraint (5.1) as,

! (5.4)

Expressed in this form, the government budget constraint requires that the current stock of government debt must be equal to the present value of current and future primary surpluses (negative deficits). A government that has a positive level of debt, must be committed to a policy of future primary surpluses, that, in present value terms, are at least as high as its current stock of debt. Otherwise, it does not satisfy its inter-temporal budget constraint.

5.1.3 The Sustainability of Budgetary Policy

The satisfaction or not of the government budget constraint, in the sense that we have defined it, determines whether a given budgetary policy is sustainable over time. Real government debt cannot be growing at a rate higher than the real interest rate. In case it is, the government follows an unsustainable budgetary policy. In what follows, we shall concentrate on budgetary policies that satisfy the sustainability criterion (5.2).

5.2 Ricardian Equivalence and the Ramsey Model

We shall now introduce a government in the Ramsey model of a representative household that we analyzed in Chapter 2. We shall assume that the government engages in primary spending and finances this primary spending through a combination of debt and taxes that satisfies the government budget constraint (5.1).

5.2.1 Ricardian Equivalence between Government Debt and Taxes

When there are taxes and a stock of government debt, the inter-temporal budget constraint of the representative household implies that the present value of its (private) consumption cannot exceed the value of its current assets (capital plus government bonds), plus the present value of its disposable labor income, i.e its after tax labor income. Thus, the inter-temporal budget constraint of the representative household is given by,

! (5.5)

C(t) is the real consumption of the representative household at time t and W(t) is its real labor income at time t. K(0) is its stock of capital and D(0) its stock of government bonds.

(5.5) can be re-written as,

! (5.6)

e−R(t ) T (t) − Cg (t)⎡⎣ ⎤⎦t=0

∞

∫ dt ≥ D(0)

e−R(t )C(t)dt ≤ K(0) + D(0) + e−R(t ) W (t) − T (t)[ ]dtt=0

∞

∫t=0

∞

∫

e−R(t )C(t)dt ≤ K(0) + D(0) + e−R(t )W (t)dtt=0

∞

∫ −t=0

∞

∫ e−R(t )T (t)dtt=0

∞

∫

!4


We assume that the government satisfies its inter-temporal budget constraint (5.1) exactly, in the sense that the present value of future taxes minus its initial debt is equal to the present value of primary government expenditure.

Substituting (5.1) in (5.6) we get,

! (5.7)

(5.7) suggests that we can express the inter-temporal budget constraint of the representative household as a function of the present value of primary government expenditure, without any reference to the method of financing it. A given present value of primary government expenditure has the same impact on the inter-temporal budget constraint of the representative household, irrespective of whether it is financed by government debt or by taxes. All that matters is the present value of primary government expenditure.

Since the path of tax revenue or the original debt does not affect the budget constraint of the representative household, nor its preferences, then the path of tax revenue or the level of government debt cannot possibly affect private consumption. Thus, (5.7) leads us to conclude that the only thing that matters for the course of private consumption is the present value of primary government expenditure, and not the method of financing it, i.e debt or taxes.

This result is known as Ricardian equivalence between debt and taxes. 1

Government bond holdings by the representative household are not considered a net addition to its wealth, as the representative household realizes that its bond holdings will be financed by future taxes of equal present value.

5.2.2 Government Expenditure, Taxes and Government Debt in the Ramsey Model

We can analyze this result in a different way, by introducing the government in the full Ramsey model of Chapter 2.

c is private consumption, k the stock of capital, d the stock of government debt, cg primary government expenditure, and τ taxes. All variables are defined in real terms, per efficiency unit of labor.

The Euler equation for consumption is not affected by introducing the government. It is given by,

(5.8)

The capital accumulation equation takes the form,

(5.9)

e−R(t )C(t)dt ≤ K(0) + e−R(t )W (t)dtt=0

∞

∫ −t=0

∞

∫ e−R(t )Cg (t)dtt=0

∞

∫

c•(t) = 1

θ[ ′f (k(t))−δ − ρ −θg]c(t)

k•(t) = f (k(t))− c(t)− cg (t)− (n + g +δ )k(t)

See Barro (1974). The term Ricardian equivalence is due to Buchanan (1976) who pointed out that the possible 1

equivalence between debt and taxes was first highlighted by Ricardo (1817).!5


Total savings in (5.9) are defined by the difference between total income and total consumption (private and public).

Finally, government debt evolves according to (5.3). Expressing government debt accumulation per efficiency unit of labor, we get,

! (5.10)

In (5.10) we have used the marginal productivity condition to substitute out for the real interest rate.

We shall examine policies with exogenous and constant primary government expenditure per efficiency unit of labor. Thus, we shall assume that the government stabilizes primary government expenditure at,

! (5.11)

We shall further assume that the government uses taxes to stabilize government debt per efficiency unit of labor. From (5.10) and (5.11), this requires a tax policy of the form,

! (5.12)

where ! is constant target level of government debt (per efficiency unit of labor).

(5.12) implies that taxes are equal to the level of primary government expenditure, plus the part of the interest payments on government debt that must be financed by taxes, so that debt per efficiency unit of labor remains constant.

Since in the representative household model the real interest rate converges to ρ+θg, taxes per efficiency unit of labor converges to the steady state value,

! (5.12΄)

Steady state taxes are equal to the level of primary government expenditure, plus the part of the interest payments on government debt that must be financed by taxes, so that debt per efficiency unit of labor remains constant. This part is equal to the difference between the steady state real interest rate and the steady state growth rate. If the target debt level is positive, then steady state taxes are higher than steady state primary government expenditure, in order to finance interest payments on government debt. Thus, with a positive level of steady state government debt, the government runs a primary surplus on the balanced growth path.

(5.11) and (5.12) imply a sustainable fiscal policy, as the government satisfies its inter-temporal budget constraint.

d•(t) = [cg (t)−τ (t)]+ [r(t)− (n + g)]d(t) = [cg (t)−τ (t)]+ [ ′f (k(t))−δ − (n + g)]d(t)

cg (t) = c_g

τ (t) = c_g+ ′f (k(t))−δ − n − g[ ]d

_

d_≥ 0

τ_= c

_g+ ρ − n − (1−θ )g[ ]d

_≥ c

_g

!6


The evolution of capital and savings per efficiency unit of labor is described by the Euler equation for consumption(5.8) and the capital accumulation equation (5.9), for constant primary government expenditure per efficiency unit of labor as in (5.11). Thus, the capital accumulation equation is given by,

! (5.9΄)

The balanced growth path and the dynamic adjustment path are presented in Figure 5.1. For comparison, we also present the equilibrium for zero primary government expenditure.

It is clear from Figure 5.1 that primary government expenditure only leads to an equal reduction in private consumption, without any other effect on real variables. An increase in primary government expenditure causes an equal reduction in private consumption due to the increase in the present value of future taxes that reduce the present value of disposable labor income of the representative household. The stock of government debt has no effect at all on private consumption, because the method of financing government expenditure does not affect the inter-temporal budget constraint of the representative household.

If the economy is out of steady state, the adjustment takes place along the unique saddle path that leads to the steady state. To the left of k* the economy is accumulating capital and this leads to a gradual increase in private consumption per efficiency unit of labor. To the right of k* the economy is de-cumulating capital, and this leads to a gradual decline in private consumption per efficiency unit of labor.

In conclusion, in the representative household model, primary government expenditure, government debt and taxes do not affect savings and the balanced growth path, nor the adjustment path towards the steady state. Primary government expenditure crowds out an equal amount of private consumption, and has no other effects on either the balanced growth path or the adjustment path. Total savings and the accumulation of capital are not affected by the level of primary government expenditure either in the short or in the long run.

5.3 Dynamic Effects of Fiscal Policy in the Blanchard Weil Model

We next move on to examine the impact of fiscal policy in an overlapping generations model with perpetual youth (Blanchard-Weil). The model was analyzed in Chapter 4. In the present chapter we introduce the government to this model.

5.3.1 The Blanchard Weil Model with Government Expenditure and Government Debt

The perpetual youth model with constant government expenditure and government debt per efficiency unit of labor, as implied by (5.11) and (5.12), is described by the following two equations:

! (5.13)

! (5.9΄)

k•(t) = f (k(t))− c(t)− c

_g− (n + g +δ )k(t)

c•(t) = [ ′f (k(t))−δ − ρ − g]c(t)− nρ[k(t)+ d

_]

k•(t) = f (k(t))− c(t)− c

_g− (n + g +δ )k(t)

!7


All variables are expressed per efficiency unit of labor. c is private consumption, k is physical capital, d is government debt, cg is primary government expenditure and τ denotes lump sum taxes.

(5.13) describes the behavior of consumers and (5.9΄) the accumulation of physical capital as the difference between total savings and equilibrium investment.

The only difference from the Ramsey model of the previous section is in equation (5.13) for the adjustment of private consumption. Since new entrants to the economy do not have accumulated savings in the form of either capital k or government bonds d, the change in private consumption depends negatively on k+d, multiplied by the product of the proportion of new entrants in total population n, and their propensity to consume out of wealth ρ. ρ(k+d) measures the difference between the average consumption of the old generations and the new generation born at t.

5.3.2 Government Debt, Taxes and Redistribution across Generations

The behavior of the model is analyzed in Figure 5.2. The balanced growth path is at point E, where both (5.13) and (5.9΄) are satisfied for constant consumption and capital per efficiency unit of labor. There is a unique saddle path leading to the balanced growth path. One can see that E implies lower consumption and capital per efficiency unit of labor than the corresponding representative household model at point R. Point R is the balanced growth path of a corresponding economy with n=0 in (5.13΄), which is the balanced growth path of a representative household economy.

One can easily show, with the help of the phase diagram in Figure 5.3, that a permanent one off increase in government debt leads to a reduction of both steady state capital and steady state private consumption. When government debt rises in a one off fashion, consumption rises to point E0 on the new saddle path, as current generations treat their higher bond holdings as an increase in their wealth. This initiates a process of de-cumulation of capital and declining private consumption, that leads the economy towards the new balanced growth path at E΄.

One can also show, with the help of the phase diagram in Figure 5.4, that a permanent increase in primary government expenditure financed by a rise in autonomous taxes, also leads to lower steady state capital and private consumption. When the increase in government expenditure occurs, private consumption falls, as current generations react to the increase in the present value of their taxes. However, the anticipated increase in the present value of taxes for current generations is lower than the increase in the present value of primary government expenditure. This is because part of the future tax burden will be shouldered by future generations. Thus, private consumption falls by less than the increase in primary government expenditure, and total savings fall relative to equilibrium investment. This starts a process capital de-cumulation and declining consumption on the new saddle path, which leads the economy to a new balanced growth path with lower steady state capital, output and consumption per effective unit of labor.

As one can deduce from this analysis, in an overlapping generations model, both the level of government debt and taxes, and primary government expenditure, affect the balanced growth path. Ricardian equivalence does not hold, as current generations know that part of the increase in the present value of taxes required to finance an increase in government debt, or primary government expenditure, will be borne by future generations. Thus there are effects on total savings and capital

!8


accumulation, as government debt and expenditure policies essentially redistribute wealth among generations.

5.3.3 A Dynamic Simulation of Fiscal Policies in the Blanchard Weil Model

The fiscal policies we have considered so far consist of one off permanent increases in either primary government expenditure or government debt, per efficiency unit of labor. This has allowed us to eliminate the dynamics of government debt accumulation, and keep our model simple, in that it consisted of one state and one control variable.

We shall now examine a more realistic description of fiscal policy in the Blanchard and Weil model, where the government chooses a level of primary government expenditure and autonomous taxes, and then allows taxes and government debt to adjust gradually, in a way that satisfies the government budget constraint.

Thus, we shall again assume that,

! (5.11)

However, we shall now assume that the government uses taxes to stabilize government debt per efficiency unit of labor only gradually and not immediately as in equation (5.12). For this it uses a tax policy of the form,

! (5.12΄΄)

where ! and ! .

! denotes autonomous taxes (per efficiency unit of labor), and ψ>0 the induced stabilizing reaction of taxes to the level of government debt. rE is the steady state real interest rate in the Blanchard Weil model. As the government accumulates debt, taxes increase gradually in order to stabilize government debt per efficiency unit of labor. Taxes according to (5.12΄΄) have two components: an autonomous component, and a debt induced component, which serves to stabilize government debt.

Substituting (5.11) and (5.12΄΄) in (5.10), government debt per efficiency unit of labor evolves according to,

! (5.10΄)

Τhere are now three parameters describing fiscal policy:

! , primary government expenditure per efficiency unit of labor, ! , autonomous taxes, and ψ, the responsiveness of taxes to government debt.

The differential equation (5.10΄) will be stable if the responsiveness of taxes to government debt ψ is higher than r(t)-n-g , which, as we have assumed, will certainly apply in the steady state.

cg (t) = c_g

τ (t) = τ_+ψ d(t)

c_g ≥ τ

_> 0 ψ > rE − n − g > 0

τ_

d•(t) = [c

_g−τ

_]+ [r(t)− (n + g)−ψ ]d(t)

c_g τ

_

!9


In what follows, we shall simulate the Blanchard Weil model of the previous sub-section, assuming a Cobb Douglas production function of the form,

! , ! , ! (5.14)

We thus simulate the model described by (5.13) and (5.9΄), using (5.14) and the assumptions about fiscal policies embodied in (5.11), (5.12΄΄) and (5.10΄). 2

This will allow us to get both a qualitative and a quantitative assessment of the full dynamic effects of tax versus debt financed increases in government expenditure, as well as debt financed cuts in autonomous taxes.

The parameter values in the simulations are as follows:

Α=1, α=0.333, ρ=0.02, θ=1, n=0.01, g=0.02, δ=0.03.

These values are the same as the ones we used in previous simulations, such as the simulations in Chapter 3.

As for the parameters of fiscal policy, we shall assume that,

! , ! and ψ=0.075.

We consider three alternative fiscal policy shocks.

First, a tax financed increase in primary government expenditure by 0.05, from 0.5 to 0.55 (Figure 5.5).

Second, a debt financed increase in primary government expenditure by 0.05, from 0.5 to 0.55 (Figure 5.6). This policy results in an increase in government debt, but also taxes, through the induced stabilizing reaction of taxes to the rise in government debt.

Third, a debt financed cut in autonomous taxes by 0.05 (Figure 5.7). This last shock amounts to a temporary tax cut, that increases government debt and eventually taxes, through the induced stabilizing reaction of taxes to the rise in government debt.

In Figure 5.5 we depict the effects of a permanent tax financed increase in primary government expenditure by 0.05 (10% of its original level). This reduces private consumption expenditure immediately, because of the increase in autonomous taxes. However, as part of the future autonomous taxes will be paid by future generations, the reduction of private consumption by current generations is lower than the increase in primary government expenditure, and total savings fall. This starts a process of de-cumulation of capital that leads the economy to a new steady state, with lower capital, output, private consumption and real wages per efficiency unit of labor, as well as a higher real interest rate. However, it is worth noting that the effects of an tax financed increase in primary government expenditure on steady state non fiscal real variables are extremely small. A 10% increase in real primary government expenditure, as the one we have considered, reduces

y(t) = Ak(t)α A > 0 0 <α <1

c_g = 0.5 τ

_= 0.45

In fact, we simulate a discrete time version of this model.2

!10


steady state real per capita output (and real wages) by only 0.07% and increases the steady state real interest rate by only 0.01 percentage points (i.e from 5.24% to 5.25%). The steady state aggregate savings rate is reduced from 27.7% to 27.6%, again a very small decline.

In Figure 5.6, we depict the effects of a debt financed increase in primary government expenditure by 0.05 (10% of its original level). This also reduces private consumption expenditure immediately, because of the anticipated future increase in taxes that will be required for debt to be eventually stabilized. However, as part of the future taxes will be paid by future generations, the reduction of private consumption by current generations is lower than the increase in primary government expenditure, and total savings fall. This starts a process of de-cumulation of capital that leads the economy to a new steady state, with lower capital, output, private consumption and real wages per efficiency unit of labor, as well as a higher real interest rate. Government debt is also increasing in the process, and ends up at more than double its initial level. It is worth noting that the effects of a debt financed increase in primary government expenditure on non fiscal steady state real variables are also extremely small, although bigger than a tax financed increase. A 10% increase in real primary government expenditure, as the one we have considered, reduces steady state real per capita output (and real wages) by only 0.21% and increases the steady state real interest rate by only 0.03 percentage points (i.e from 5.24% to 5.27%). The steady state aggregate savings rate is reduced from 27.7% to 27.6%, again a very small decline. Thus, although the real effects of a debt financed increase in primary government expenditure on per capita real output and the real interest rate are almost three times as high as the effect of an equivalent tax financed increase, they remain extremely small.

Finally, in Figure 5.7 we depict the effects of debt financed cut in autonomous taxes by 0.045 (10% of their original level). This increases private consumption expenditure immediately, because current generations anticipate that the future increases in taxes that will be required for debt to be stabilized will be paid in part by future generations. The increase in private consumption and the associated reduction in savings starts a process of de-cumulation of capital that leads the economy to a new steady state, with lower capital, output, private consumption and real wages per efficiency unit of labor, as well as a higher real interest rate. Government debt is also increasing in the process, and ends up at more than double its initial level. It is worth noting that the effects of a debt financed cut in autonomous taxes on non fiscal real variables are also extremely small. A 10% reduction in autonomous taxes, as the one we have considered, reduces steady state real per capita output (and real wages) by only 0.14% and increases the steady state real interest rate by only 0.02 percentage points (i.e from 5.24% to 5.26%). The steady state aggregate savings rate is reduced from 27.7% to 27.6%, again a very small decline. Thus, the real effects of a debt financed cut in autonomous taxes are extremely small, even smaller than a debt financed rise in primary government expenditure.

The results of these simulations are extremely valuable. They suggest that although Ricardian equivalence does not hold in overlapping generations models, the deviations from Ricardian equivalence imply very small real effects on steady state real variables such as the savings rate, or per capita real output, real wages and real interest rates.

This should not be very surprising, as the non-Ricardian effects in overlapping generations models depend on the product of two quantitatively small parameters. Population growth, which is assumed to take place through the entry of new generations, and the pure rate of time preference, which determines the proportion of total assets consumed by households. With a population growth rate of

!11


1% per annum, and a pure rate of time preference of 2% per annum, as we have assumed in the simulations, the product of the two is only 0.2%, a small number indeed. 5.4 The Dynamic Effects of Distortionary Taxation

Until now we have assumed that taxation takes the form of lump sum taxes that do not distort factor prices and relative prices faced by households and business firms. However, lump sum taxes are very rare. Most forms of taxation, such as income and consumption taxes are levied in ways that distort the incentives of households and firms to work, save and invest. In this section we shall investigate the dynamic effects of such distortionary taxes in the representative household model.

5.4.1 Distortionary and Non Distortionary Taxes

To keep things simple, we will assume a government which runs a continuously balanced budget and has no government debt. The government engages in primary government expenditure and transfers to households, and levies taxes on income from capital and labor, business profits before interest and depreciation payments, and on the consumption of households. Thus, in every instant, the government budget constraint per efficiency unit of labor is given by,

! (5.15)

where, cg is primary government expenditure, v real transfers to households and firms, τw the tax rate on labor income, τk the tax rate on capital income, τc the tax rate on consumption and τf the tax rate on business profits, before interest and depreciation payments. All variables, apart from tax rates and the real interest rate r are defined per efficiency unit of labor.

The existence of income and consumption tax rates and government transfers affects the inter-temporal budget constraints of both households and firms, and thus their optimal savings and investment decisions. The first order condition for the maximization of profits by firms now takes the form,

! (5.16)

The Euler equation for consumption of the representative household now takes the form,

! (5.17)

From (5.16) and (5.17) it follows that,

! (5.18)

The accumulation equation for capital is not affected by the existence of distortionary taxes, as, from the government budget constraint (5.15), the revenue from distortionary taxes minus transfers, is equal to primary government expenditure. Thus, the accumulation of capital (per efficiency unit of labor) is determined by an equation of the form,

cg (t)+ v(t) = τ ww(t)+τ kr(t)k(t)+τ cc(t)+τ f f (k(t))−w(t)( )

(1−τ f ) ′f (k(t)) = r(t)+δ

c•(t) = 1

θ[(1− τ k )r(t) − ρ −θg]c(t)

c•(t) = 1

θ[(1−τ k )(1−τ f ) ′f (k(t))− (1−τ k )δ − ρ −θg]c(t)

!12


! (5.9΄)

The behavior of the economy is determined by (5.18) and (5.9΄). The only distortionary taxes that enter these two equations are the tax rate on interest income τk and the tax rate on the profits of firms before interest τf.

The tax rate on labor income τw does not affect any of the first order conditions, and thus does not affect the behavior of the economy. The reason is that we have assumed that labor supply is inelastic, as every household member supplies one unit of labor, irrespective of the real wage. If labor supply was elastic, then taxes on labor income would have real effects.

In addition, the consumption tax τc does not enter the Euler equation for consumption, as we have assumed that this tax rate is constant and does not affect the inter-temporal substitution of consumption (savings). In, addition, since labor supply is also assumed exogenous, the tax rate on consumption does not affect labor market incentives either (substitution between consumption and leisure).

As a result, in the Ramsey model with inelastic labor supply, as we have assumed throughout, the only distortionary taxes are taxes on income from capital and taxes on profits of business firms before interest and depreciation. All other taxes are non-distortionary.

5.4.2 Dynamic Effects of Capital Income Taxation

The dynamic effects of capital income taxes are analyzed in Figure 5.5. We assume that initially the taxation of income from capital is zero and the economy rests at the balanced growth path E. The government announces an unanticipated capital income tax at a rate τk . The proceeds are returned to households in the form of transfer payments. The equilibrium consumption locus moves to the right, as in the new balanced growth path the pre-tax real interest rate must rise, something that requires a lower steady state capital stock per efficiency unit of labor. As the capital stock is a predetermined variable, the pre-tax real interest rate is also a predetermined variable. The introduction of the tax thus causes a reduction in post tax real interest rates for households. Consumption rises to c0 and savings fall immediately. The economy enters into a process of capital de-cumulation, rising real interest rates and falling consumption. In the new balanced growth path at E(τk) the capital stock per efficiency unit of labor is lower and so is total output and private consumption.

A similar process will take place if there is an increase in the tax rate on business profits before interest. This will initially cause a fall in the real interest paid out to households, a temporary increase in private consumption, a process of de-cumulation of capital and adjustment to a new balanced growth path with a lower capital stock, lower output and income, lower real wages and lower consumption per efficiency unit of labor.

The dynamic effects of distortionary taxation would be qualitatively similar in overlapping generations models, such as the model of Blanchard and Weil.

5.4.3 A Dynamic Simulation of an Increase in Capital Income Taxation

k•(t) = f (k(t))− c(t)− c

_g− (n + g +δ )k(t)

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In order to examine quantitatively the dynamic effects of an increase in capital income taxation in the Ramsey model, we can simulate, for the specific values of the parameters of the model assumed so far, the transition from a balanced growth path without capital income taxation to a balanced growth path after the introduction of capital income taxation.

The parameter values used in the simulations are as follows: Α=1, α=0.333, ρ=0.02, θ=1, n=0.01, g=0.02, δ=0.03.

These values are the same as those used in the simulations of the Ramsey model in Chapter 2.

In the simulation of Figure 5.9, the economy is on its original balanced growth path, without capital income taxation. In period 1 the government imposes a previously unanticipated 10% tax on interest income (increase of τk). This increase, as predicted theoretically in the analysis of Figure 5.8, leads to a decrease in the net real interest rate enjoyed by households. This causes an increase in consumption and a fall in the savings rate, which initiate a process of capital de-cumulation, a gradual decline in real output and real wages, and a gradual increase in the pre-tax real interest rate. The reduction in real wages and the increase in the pre-tax real interest rate is a result of the declining capital stock, which causes a falling marginal product of labor and a rising marginal product of capital. The economy gradually converges to a new balanced growth path. In this, capital per efficiency unit of labor is lower by approximately 8.9% compared to the original balanced growth path, output and real wages are lower by 3.0%, consumption is lower by 0.7% (due to the decline in the saving rate), while the real rate has increased by 0.44 percentage points, or approximately 10%. The steady state savings rate, which is endogenous in this model, falls from 28.5% to 26.8%.

As one can deduce from these simulations, even a relatively low rate of capital income taxation causes relatively large declines in per capita per capita output and income, as it leads to a significant reduction of savings and capital accumulation. Similar negative effects would apply to tax rates on business profits before the deduction of interest and depreciation.

5.5 Conclusions

In the present chapter we first introduced the inter-temporal government budget constraint and analyzed the conditions for government debt sustainability. We also analyzed the dynamic effects of government debt and primary government expenditure in the representative household model of Ramsey and the overlapping generations model of Blanchard and Weil. We finally analyzed the dynamic impact of distortionary taxes.

We concluded that in the representative household model without distortionary taxes, fiscal policy has no effects on either the convergence process or the balanced growth path. The only fiscal variable that matters for the path of private consumption is the present value of primary government expenditure, which reduces the present value of private consumption by exactly the same amount. The method of financing primary government expenditure, such as government debt and (non-distortionary) taxes does not affect private consumption, or the adjustment and balanced growth path of all other real variables. This result is known as Ricardian equivalence between lump sum taxes and government debt. Holdings of government bonds by the representative household are not

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considered as wealth, and do not affect household consumption, since the representative household realizes that government bonds will be financed by future taxes of equal present value.

The Ricardian equivalence result does not apply to overlapping generations models. Both the level of government debt, and primary government expenditure affect both the balanced growth path and the adjustment path. This is because current generations realize that part of the future taxes that will finance either primary government expenditure, or interest on the government debt, will be shouldered by future generations. Consequently, both primary government expenditure and government debt lead to a reduction in aggregate savings, and lead to a reduction of steady state capital and private consumption. A dynamic simulation of the Blanchard Weil model of overlapping generations suggests however that the effects of deviations from Ricardian equivalence are relatively small in this model.

We finally analyzed the dynamic impact of distortionary taxes, as taxes are rarely non-distortionary. In the representative household and overlapping generations that we have considered, labor supply is exogenous. Consequently, tax rates on income from employment or constant consumption tax rates do not affect employment and savings, with the result that they do not affect either the adjustment path or the balanced growth path. On the other hand, tax rates on capital income or business earnings before interest and depreciation are distortionary, and have negative effects on private savings and investment, the accumulation of capital, real output, real wages and real interest rates. A dynamic simulation of the Ramsey model, for plausible parameter values, suggests that these effects of capital income taxation may be quantitatively large.

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Figure 5.1 Primary Government Expenditure in the Ramsey Model

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k

k*

c=0

k=0

c*

-cg

E

c


Figure 5.2 Primary Government Expenditure and Debt in the Blanchard Weil Model

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k

c

k*

c=0

k=0

c*

-cg

kR*

E

R


Figure 5.3 An Increase in Government Debt in the Blanchard Weil Model

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k

c

k*

c=0

k=0

c*

-cg

kR*

ER

E΄

Ε0


Figure 5.4 An Increase in Primary Government Expenditure in the Blanchard Weil Model

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k

c

k*

c=0

k=0

c*

-cg

kR*

E R

E΄ Ε0


Figure 5.5 Dynamic Simulation of a Tax Financed Increase in Primary Government Expenditure

in the Blanchard Weil Model

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Figure 5.6 Dynamic Simulation of a Debt Financed Increase in Primary Government

Expenditure in the Blanchard Weil Model

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Figure 5.7 Dynamic Simulation of a Debt Financed Cut in Autonomous Taxes

in the Blanchard Weil Model

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Figure 5.8 Capital Income Taxation in the Ramsey Model

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k

k*

c=0

k=0

c*

-cg

E

k*(τκ)

c*(τκ)

c c0

E(τκ)


Figure 5.9 Dynamic Simulation of the Effects of a 10% Tax on Interest Income

in the Ramsey Model

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References

Barro R.J. (1974), “Are Government Bonds Net Wealth”, Journal of Political Economy, 82, pp. 1095-1117.

Blanchard O.J. (1985), “Debts, Deficits and Finite Horizons”, Journal of Political Economy, 93, pp. 223-247.

Buchanan J.M. (1976), “Barro on the Ricardian Equivalence Theorem”, Journal of Political Economy, 84, pp. 337-342.

Diamond P. (1965), “National Debt in a Neoclassical Growth Model”, American Economic Review, 55, pp. 1126-1150.

Ricardo D. (1817), Principles of Political Economy and Taxation, London. Ramsey F. (1928), “A Mathematical Theory of Saving”, Economic Journal, 38, pp. 543-559. Weil P. (1989), “Overlapping Families of Infinitely-Lived Agents”, Journal of Public Economics,

38, pp. 183-198.

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Chapter 5 Fiscal Policy and Economic Growth · depreciation, have a negative impact on savings and investment. Such taxes affect savings and capital accumulation negatively, and,