Fiscal policy and saving under distortionary taxation

Journal of Monetary Economics 42 (1998) 25—45

Fiscal policy and saving under distortionary taxation

Momi Dahan!, Zvi Hercowitz",*! Bank of Israel, Jerusalem, Israel

" The Eitan Berglas School of Economics, Tel Aviv University, Tel Aviv 69978, Israel and Bank of Israel,Jerusalem, Israel

Received 14 August 1996; received in revised form 9 July 1997; accepted 4 September 1997

Abstract

An empirical investigation of the effects of fiscal policy on saving is carried out usingIsraeli data, which display large variability in both the saving rate and the fiscal variables.The framework is a small open economy model with distortionary taxation. The theore-tical analysis of the partial effect of each fiscal variable on the national saving rate takesinto account the necessary adjustment in future taxes. The present model predicts, forexample, that the income-tax rate should have a negative effect on saving — in contrast tothe Keynesian view — and that transfer payments and interest payments on the publicdebt should have positive effects — in contrast to the Ricardian view under lump-sumtaxation. The empirical results partly support the predictions of the model — in particularfor the income-tax rate. The methodology consists of two steps. First, quantitativepredictions are obtained via simulation, and then the simulated effects are compared withthe estimated coefficients. ( 1998 Elsevier Science B.V. All rights reserved.

JEL classification: E62

Keywords: Fiscal policy; Distortionary taxation

1. Introduction

The national saving rate in Israel is highly volatile, ranging from 13% to 28%during 1960—1994 (Fig. 1). This is consistent with a model of a small openeconomy subject to large exogenous shocks. The role of saving as a shock

*Corresponding author. E-mail: [email protected]

0304-3932/98/$19.00 ( 1998 Elsevier Science B.V. All rights reserved.PII S 0 3 0 4 - 3 9 3 2 ( 9 8 ) 0 0 0 1 4 - 2

Fig. 1. National savings as share of GDP.

Fig. 2. Defence expenditure as share of GDP.

absorber can be observed, for example, during and after the main war years, theSix Days War in 1967 and the Yom Kippur War at the end of 1973, when thesaving rate declined dramatically. The corresponding increases in defense spend-ing as a share of GDP can be observed in Fig. 2. Another example is the1984—1986 episode, when the high saving rates were accompanied by unusuallylarge unilateral transfers from abroad to the public sector, as shown in Fig. 3.In 1985 and 1986, these transfers reflect economic assistance from the US

26 M. Dahan, Z. Hercowitz / Journal of Monetary Economics 42 (1998) 25–45

Fig. 3. Unilateral transfers to the public sector as share of GDP.

Fig. 4. Income tax rate.

government, following the drastic economic stabilization program of July 1985.Tax rates also underwent dramatic changes during the 1960—1994 sample, asexpected from the development of the other fiscal variables. This is shown inFigs. 4 and 5, which display income and consumption tax rates, respectively.Interestingly, the consumption tax rate shows sharp swings, e.g. in 1981, whichseem unrelated to financing needs.

The large variability of the fiscal variables and the small open economycharacter of the Israeli economy — which imply that saving should be verysensitive to shocks — make it a potentially interesting case for an econometric

M. Dahan, Z. Hercowitz / Journal of Monetary Economics 42 (1998) 25–45 27

Fig. 5. Consumption tax rate.

investigation of the effects of fiscal variables on saving. The present paperpursues this line.1

The theoretical framework used in this analysis is a small open economymodel. Fiscal policy includes an adjustment mechanism, which means that thepartial effect of each current fiscal variable is analyzed in conjunction with a rulefor distortionary tax adjustment, as in Dotsey (1994). This implies that thecurrent effect of an increase in spending should also reflect the expectation ofa corresponding future increase in tax rates. The fiscal adjustment rule adoptedhere is income-tax smoothing with a white noise error. Income-tax smoothing isarbitrary in the present context. The idea, of course, rests on Barro (1979), wheretax smoothing minimizes the deadweight loss from taxation. The error in taxsmoothing is dictated by econometric considerations. A consumption tax is alsoincorporated, along with a calibrated rule for the tax structure.

To illustrate the econometric implications of the present framework, considera regression of the national saving rate on government spending variables,income and consumption tax rates, and relevant non-fiscal variables. Take, forexample, the coefficient of the income-tax rate. The present analysis predicts thatthis coefficient should be negative, in contrast to the standard Keynesian view, inwhich higher income taxes reduce consumption and increase the national savingrate. Basically, the negative effect can be explained as follows: given that allother fiscal variables are held constant, an exogenous income-tax increase (an

1An early analysis of the way fiscal policies affect macroeconomic outcomes under the neoclassi-cal approach, which the present paper follows, is Aschauer and Greenwood (1985). Kotlikoff (1984),Boskin and Kotlikoff (1985), and others focus on the saving rate.


error in tax-smoothing) should be temporary.2 In response, current labour effort(and hence output) are low relative to future labour and output, inducinga decline in current national saving.

Another example is the coefficient of government transfers to the public (or ofinterest payments on the domestic public debt). This coefficient should be zero ifone considers only the direct effect of transferring funds from one sector of theeconomy to another. However, since current tax rates are included in theregression, and are thus held constant, transfers today signal a future increase inthe smoothed income-tax rate. This depresses expected future income because oflower current investment and lower future labour. Correspondingly, currentincome is relatively high, and hence it is accompanied by higher saving, implyingthat transfers should have a positive coefficient.

The present econometric analysis of fiscal effects on savings is related to theempirical literature on the Ricardian equivalence, surveyed in Seater (1993). Ina typical regression equation in this literature, of consumption on governmentspending, tax rates, the public debt, etc., Ricardian equivalence is rejected if thedebt has a significant coefficient. In the present framework, the partial effect ofthe debt (or interest payments) on saving, holding constant the current tax rates,is expected to be positive because it signals a future tax rate increase.

The paper is organized as follows. Section 2 presents the model and Section 3discusses the empirical equation implied by this framework. The methodologyfollowed thereafter consists of two steps. First, the model is calibrated andsimulated in Section 4 in order to obtain predictions for the parameter values inthe empirical equation. Then the model is estimated in Section 5 and theempirical results are compared with the model’s predictions. Section 6 con-cludes the paper.

2. The model

2.1. The economic environment

Consider a competitive small open economy with a private sector, composedof a large number of identical agents, and a government. Capital is mobileinternationally, but labour is not.

The utility function of the representative household is

E0

=+t/0

btº(Ct,¸

t), 0(b(1 (2.1)

2More precisely, the expected future tax rate should be slightly lower than the rate before thechange.


with

º(Ct,¸

t)"h lnC

t#(1!h) ln (1!¸

t), 0(h(1, (2.2)

where Ctand ¸

trepresent consumption and labour, respectively.

The production of final output, ½t, requires the services of labour and capital,

Kt~1

, predetermined from the previous period. The production technology isthen described by

½t"F(K

t~1,¸

t,zt)"exp(z

t)Ka

t~1¸1~at

, 0(a(1, (2.3)

where ztis a stochastic productivity shock.

Capital accumulation depends on gross investment, It, and on the deprecia-

tion rate 0(d(1. The capital evolution equation is then:

Kt"(1!d)K

t~1#I

t. (2.4)

Changing the capital stock involves adjustment costs of the form

Ut"U(K

t,K

t~1)"

/

2[(K

t!fK

t~1)/K

t~1]2, /,f'0.

The economy faces a perfect world capital market, where borrowing andlending at time t can be undertaken at the constant real interest rate r"1/b!1.Given no capital controls, the domestic real interest equals r. The net stock offoreign bonds in the economy at the beginning of period t is B

t~1, the sum of the

private component Bpt~1

and the government’s component Bgt~1

. There are alsodomestic bonds: the private sector holds Dp

t~1of these bonds, and the public

sector holds Dgt~1

"!Dpt~1

.The government levies taxes on income at rate qy

t, and on consumption at the

rate qct. Government income also includes º¹g

t, unilateral transfers from abroad.

Government expenditures consist of purchases of goods and services, Gt, which

have the permanent component G13t

and the transitory component G53t, and

lump-sum transfers to the public, »t. No government investment is assumed.

Government saving is then given by

Sgt"qy

t½

t#qc

tC

t#º¹g

t#r(Dg

t~1#Bg

t~1)!G

t!»

t. (2.5)

Private saving is, correspondingly

Spt"(1!qy

t)½

t#º¹p

t#»

t#r(Dp

t~1#Bp

t~1)!(1#qc

t)C

t, (2.6)

where º¹pt

are unilateral transfers from abroad to the private sector.National saving is then obtained by adding Eqs. (2.5) and (2.6):

St"½

t#º¹p

t#º¹g

t#r(Bp

t~1#Bg

t~1)!C

t!G

t. (2.7)


Defining g13t,G13

t/½

t, g53

t,G53

t/½

t, etc., the following variables are considered

exogenous and governed by the autoregressive processes:

g13t"(1!o

1)g13#o

1g13t~1

#j1t, o

1"1,

g53t"(1!o

2)g53#o

2g53t~1

#j2t, 0(o

2(1,

vt"(1!o

3)vN#o

3vt~1

#j3t, 0(o

3(1,

utgt"(1!o

4)utg#o

4utg

t~1#j

4t, 0(o

4(1,

utpt"(1!o

5)utp#o

5utp

t~1#j

5t, 0(o

5(1

and

zt"o

6zt~1

#j6t, 0(o

6(1.

A time trend in the productivity factor zt, and hence in output, does not affect

saving, and hence is not included. It is assumed that Mj1t,2, j

6tN are serially

independent with zero mean.

2.2. Equilibrium

2.2.1. Government behaviourThe government is not an optimizing entity in this model. Its behaviour is

characterized as follows. First, it faces the intertemporal budget constraint:

=+t/0

Rt[qy

t½

t#qc

tC

t#º¹g

t!G

t!»

t]#(1#r)(Dg

~1#Bg

~1)"0, (2.8)

where R0"1 and R

j`1"R

j/(1#r).

The next issue is the specification of the tax structure, which should beconsistent with its actual behavior. One theoretical possibility is that incomeand consumption tax rates are smoothed jointly, given the innovations in otherfiscal variables. This would lead to a tight positive correlation between the twotax rates. Figs. 4 and 5 show these two tax rates (its construction is reported inSection 4) are not tightly positively correlated. On the contrary, the correlationcoefficient is !0.26. Hence, joint smoothing is not a realistic specification. Thenegative correlation suggests that if one tax rate is changed exogenously (i.e. notbecause of budget finance needs), the other moves in the opposite direction tocomply with the intertemporal budget constraint. Historical evidence suggeststhat it is the consumption tax rate that evolves exogenously, i.e. in a way that itis not dictated by spending needs. For example, the large decline in the con-sumption tax in 1981, shown in Fig. 5, was due to a massive increase inconsumption subsidies and a decrease in indirect taxation. The purpose of this


policy was peculiar: to reduce the inflation rate (130% in 1980) by lowering thecost of consumption to the public.3 Fig. 5 also shows that starting in 1976 theconsumption tax has an upward trend, which, for the reason mentioned abovewas interrupted in 1981, and has accelerated since then. This trend is due to theintroduction of a value-added tax in 1976, which is levied only on consumptionproduction, following its adoption in European countries. This event can also betreated as exogenous to current financing needs; it reflects an attempt toreduce overall tax distortion.4 Econometric evidence also indicates thattaxation income does appear to be related to government spending needs, whileconsumption taxation does not.5 Furthermore, there is some evidence of in-come-tax smoothing (see footnote 6). We therefore adopt the following twoassumptions:

1. qctis exogenous, and treated in the same way as the other exogenous variables:

qct"(1!o

7)qc#o

7j7t, 0(o

7(1.

2. qyt

is smoothed with a random error. This implies that if is the smoothincome-tax rate satisfying Eq. (2.8), given time-t information, the current taxrate qy

tequals #g

t, where g

tis white noise. Correspondingly, the planned

(qyt)*,qy

t`1"qy

t`22is adjusted in the opposite direction to g

t(Note that

the computation of and (qyt)* should take into account their effects on the

½’s in Eq. (2.8)). The econometric importance of the error is elaboratedin Section 3. This tax rule is arbitrary in the present context, although

3 “The government’s policy in 1981 was aimed at cooling inflation through direct action on theprice front (subsidies and taxes) and by dampening inflationary expectations”. ‘Bank of Israel,Annual Report 1981, May 1982, p. 84.’ Inflation did decline from 130% in 1980 to 117% in 1981, butincreased again in 1982 to reach 370% in 1984.

4 “The law proposed is part of a proposed reform of the tax system in Israel. In the framework ofthis reform, direct taxation will be reduced, and in particular the income tax, and the tax base ofdirect and indirect taxes will be enlarged”. From the introduction to The Value Added Tax Law,1975, Law Proposal d 1178 (authors’ translation from Hebrew).

5 In the following regressions g is defined as the sum of all current government spending less utg:

qyt"!0.85#0.13 g

t#0.40 g

t~1, R2"0.73,

(!0.33) (0.94) (3.10)

qct"!0.23!0.20 g

t!0.06 g

t~1, R2"0.18,

(!5.53) (0.84) (0.28)

where t-statistics are in parentheses. Income taxation is found to be related to budget financing, andconsumption taxation is not.


consistent with the behaviour of the income-tax rate in the Israeli data.6 Boththe current qy

tand the planned (qy

t)* are public information, and hence (qy

t)*

represents the expected future income-tax rate as of time t.

2.2.2. The representative private sector agentThe dynamic programming problem facing the representative agent is

»[qyt,(qy

t)*,qc

t,utp

t,Bp

t~1,Dp

t~1,K

t~1]

" maxCt,Lt,Bp

t`Dpt,Kt

Mº(Ct,¸

t)#E

t»[qy

t`1,(qy

t`1)*,qc

t`1,utp

t`1,Bpt,Dp

t,K

t]N, (2.9)

subject to

Ct"

1

1#qct

[F(Kt~1

,¸t,zt)(1!qy

t#v

t#utp

t)#(1!d)K

t~1!K

t!U

t]

#(1#r)(Dpt~1

#Bpt~1

)!(Dpt#Bp

t)], (2.10)

and the solvency constraint limt?=

(Dpt#Bp

t)/R

t"0.

Note that (qyt)* is a state variable, representing current information about the

smooth income-tax rate planned for period t#1 onwards.

2.2.3. SummaryThe variables in the model can be clustered in three groups:

1. Exogenous variables: g13t, g53

t, v

t, utg

t, utp

t, z

t,qct

and qyt

(the latter because oferror g

t)

2. Endogenous, but predetermined state variables: Bpt~1

, Bgt~1

, Dgt~1

(or !Dpt~1

)and K

t~1,

3. Endogenous variables: Ct, ¸

t, Bp

t, Bg

t, Dg

t(or !Dp

t) and K

t.

6Changes in the tax rate should be white noise under exact tax-smoothing. In the presence oferror g

t, which is corrected in the following period, changes in the tax rate should have a small

negative serial correlation. The regression results obtained using annual data for the 1960—1994period are

*qyt"0.41!0.02 *qy

t~1(0.83) (0.09)

.

(t-statistics in parentheses). This evidence seems to support exact tax smoothing rather thansmoothing with an error. However, given that the tax reversal is theoretically very small, thisregression does not contradict the assumption of an error.


Dividing the national saving Eq. (2.7) by ½t, the national saving rate (defined

as national saving as a percentage of GDP) can be expressed as

st"1#utp

t#utg

t#

r(Bpt~1

#Bgt~1

)!Ct

F(Kt~1

,¸t,zt)

!gt, (2.11)

where Ctand ¸

tdepend on the variables in (1) and (2) above.

3. The empirical equation

The formulation of the regression equation for the national saving rate isbased on a linearization of Eq. (2.11), using the exogenous and predeterminedvariables as independent variables. For convenience, the independent variablesare divided into two groups: fiscal — i.e. the components of government saving;and nonfiscal:

st"a

0#a

1g13t#a

2g53t#a

3vt#a

4qyt#a

5qct#a

6utg

t#a

7rdg

t~1

#a8rbg

t~1#cx

t#e

t, (3.1)

where xt"Mutp

t,zt,bp

t~1,k

t~1N is the vector of nonfiscal variables, c is the corres-

ponding vector of coefficients and etis an error term, which is discussed below.

Given the long-run trend present in the actual data, the state variablesBpt~1

, Dgt~1

, Bgt~1

and Kt~1

are expressed as ratios to lagged output, i.e.,bpt~1

"Bpt~1

/½t~1

, etc.7Note that the coefficient on each fiscal variable captures a partial effect with

respect to the other current budget variables, which are held constant by virtueof their inclusion in the equation. However, future budget variables are not heldconstant. This implies, for example, that the coefficients of the spending vari-ables reflect two combined effects: (a) the direct effect of the change in currentspending, holding qy

tand the other current budget variables constant, and (b) an

indirect effect of the expected adjustment of qyt`1

to the new level.The fact that the other current fiscal variables are held constant implies that

each coefficient a in Eq. (3.1) refers to the short-run effect — i.e. the impact in thesame period. The dynamic effect, or ‘impulse response’ pattern, can be com-puted, in principle, by adding the effects of the resulting evolution of theincome-tax rate and other state variables.8

7Eq. (3.1) is interpreted as a linearization of Eq. (2.11) at the steady state. This is important for thesimulation of the coefficient values in Section 4, where the simulation was performed from the steadystate.

8This implies, of course, that Eq. (3.1) by itself cannot be used to compute the long-run effect ofaltering only one of the fiscal variables. In the long run, the fiscal variables are linked by a zero sumconstraint.


Note that the error in income-tax smoothing has an important implication forthe interpretation of a

4(the coefficient of qy

t). If there were exact tax smoothing,

qyt

would be an exact (but, in general, nonlinear) function of the other fiscalvariables. In this case, a

4could not be interpreted as a partial derivative because

qytwould vary only if there is a change in some other fiscal variable. The error in

tax smoothing breaks this exact relationship between qyt

and the other fiscalvariables, allowing for a partial effect interpretation of the income-tax ratecoefficient.

Finally, consider error et. The model says nothing on the properties of this

term, which reflects many macroeconomic factors omitted from the model— such as shifts in the terms of trade, financial changes, technological progressother than that captured by z

t, immigration, etc. The high likelihood that e

tis

serially correlated raises the following econometric problem. The fiscal variablesare strongly serially correlated, as can be seen in Figs. 2—5. If both the fiscalvariables and the error term follow AR processes, they are weighted infinitesums of past innovations. Hence, for the fiscal variables to be exogenous, i.e.uncorrelated with e

t, innovations to these policy decisions should be indepen-

dent at all leads and lags from the innovations in factors represented by the errorterm. This is obviously a very strong assumption. Finding instrumental vari-ables is highly problematic because they, too, should be serially uncorrelated— in order not to be subject to the same problem as the fiscal variables, anduncorrelated with the array of factors represented by e

t. Lagged independent

variables are not valid instruments either under serial correlation. Furthermore,since the theory implies that saving serves as a shock absorber, the effects of theindependent variables should take place contemporaneously, and hence laggedvariables are theoretically not useful instruments. The simultaneity problem canbe alleviated, however, if Eq. (3.1) is estimated in first differences

*st"a

1*g13

t#a

2*g53

t#a

3*v

t#a

4*qy

t#a

5*qc

t#a

6*utg

t

#a7*(rdg

t~1)#a

8*(rbg

t~1)#c*x

t#*e

t, (3.2)

where *st"s

t!s

t~1, etc. If *e

tturns out to be serially uncorrelated, the

exogeneity requirement in this case is much weaker: independence of the currentchanges in the regressors from the current innovation in e

t.9 If *e

tturns out to

have positive serial correlation, further correction for serial correlation is neces-sary, not only for the usual reason, but also, as explained above, to alleviatea possible simultaneity bias. Negative serial correlation in *e

twould suggest

over-differencing.

9Note that if the regressors in levels are correlated with the true et, the residuals from the

regression in levels will probably not reflect the true serial properties of et.


4. Determination of the saving rate

This section provides quantitative predictions for the coefficients in the savingrate equation (3.2) by simulating a realistically calibrated version of the model.The procedure adopted is as follows: (a) the model is calibrated to Israeli data;(b) using the deterministic version of the model, all the exogenous and predeter-mined variables are shifted one at a time by one unit, using the steady state asthe initial situation. The resulting changes in the current saving rate correspondto the coefficients in Eq. (3.2), or Eq. (3.1), where the linearization of Eq. (2.11) istaken at the steady state. In this computation, expected future income-tax ratesare adjusted to satisfy the intertemporal budget constraint of the government,and the expected future path of each exogenous variable depends on its autocor-relation coefficient.10

4.1. The data

The sample used in the calibration of the model in this section and in itsestimation in Section 5 below, is composed of annual Israeli data from 1960 to1994. The following empirical counterparts to the theoretical variables areconstructed, unless otherwise specified, by dividing nominal values by nominalGDP.

s gross national saving,g13 no empirical counterpart found. This variable is nevertheless in-

cluded in the simulation for comparison purposes,g53 in the econometric implementation this variable was separated into

two components of government consumption:g$%& defense expenditures,gc civilian spending on goods and services,v gross government transfer payments to the private sector (excluding

interest payments on the domestic debt), less import duties andproperty taxes (these are not included in the calculation of incomeand consumption tax rates),

qy income-tax rate, calculated by dividing the revenue from incometaxation and social insurance taxes by national income at factorprices,

10An alternative route would be to simulate the model stochastically, producing artificial seriesfor all the variables involved, and then to perform the regression of Eq. (3.2). The main complicationin this procedure is to incorporate the intertemporal budget constraint of the government, and theadjustment of future taxes.


qc consumption-tax rate, computed as the ratio of revenue from in-direct taxes on domestic production to total consumption before tax.This revenue includes a small component of taxes on domestically-produced investment goods. Import duties, however, include a largecomponent from investment goods, and were therefore excluded,

utg unilateral transfers from abroad to the public sector,!rdg

~1net interest payments on the domestic public debt (current nominalinterest payments multiplied by current nominal GDP multiplied bythe gross growth rate of real GDP),11

!rbg~1

net interest payments on the external public debt (computed sim-ilarly to rdg

~1),

utp unilateral transfers from abroad to the private sector,k~1

net capital stock in the business sector (stock in constant prices at theend of t!1, divided by real GDP at t!1),

z ‘Solow residual’ computed from the production function in Eq. (2.3),the gross product of the business sector, k

~1and hours of work in

the business sector,bp~1

private net foreign assets.

4.2. Calibration

Values must be assigned to the following parameters and initial conditions:Preferences: b and h,Technology: a,d,/, and f,Exogenous variables: g53,qy,qc,utg and utp (determining together vN ), o

2,2,o

7,

World interest rate: r,Initial state variables: bp

~1,bg

~1,dg

~1, (k

~1follows in the steady state from the

parameter values and the other state variables).Standard values are assigned to the parameters:

b"0.96, r"1/b!1,

a"0.35, capital share in gross income,

d"0.08.

The rest of the parameter values are determined as follows.

h"0.75.

11What needs to be computed is the actual counterpart of rdg~1

"rDg~1

/½~1

, while the availabledata on nominal interest payments can be expressed as rDg

~1P, where P is the current price level.

Hence, the data transformation has the form:

rDg~1

P

P½

½

½~1

"rbg~1

.


This value is determined so that the compensated real wage elasticity oflabour supply at the steady state equals 0.5, which is a relatively low elasticityfor aggregate labour supply. The purpose of imposing low elasticity is to obtainconservative model effects of distortionary taxation on labour and capitalaccumulation. The procedure is to find h so that the steady-state ¸"2

3, given

that under the present utility function, that elasticity equals (1!¸)/¸. Thesevalues for h and ¸ are high (and the implied elasticity low) compared to valuesobtained in the literature to match the observed average share of hours workedin the total non-sleeping time available to the working-age population.

g53"0.34 o2"0.86, 0.85

vN"0.054 o3"1

utg"0.07 o4"0.74

qy"0.26

qc"0.13 o7"0.87

utp"0.05 o5"0.77, o

6"0.91

bp~1

"!0.12

bg~1

"!0.30

dg~1

"!1.1

The first column contains sample averages (except for vN ) and the secondcontains sample autocorrelations. The estimate of vN is computed residually sothat the initial government budget is balanced. The two estimates of o

2were

obtained with g$%& and gc, respectively. The hypothesis that o3"1 cannot be

rejected, and hence o3

is set equal to one. The parameter o6"0.91 is the

autocorrelation coefficient of z. Given the unavailability of good data on thestock of the internal debt, the value dg

~1"!1.1 is obtained indirectly, dividing

the average of the corresponding interest payments/GDP ratio by r"0.04.Finally, the parameter values in the adjustment costs function are the follow-

ing. Given the assumption of zero trend, f is set equal to one. This implies that ifthe capital stock does not change, the adjustment cost is zero. The parameter/ was chosen so that when a permanent change occurs, it takes 8—10 years forthe capital stock to reach the neighborhood of the new steady state value.

4.3. Model simulation

First, given the above parameter values and initial state variables, the corres-ponding steady state is computed. If the first period of the dynamic simulation isdate t, the economy is at the steady state in t!1. Then, one by one, the variablesaffecting the saving rate in Eq. (3.2) are altered at time t by one unit, and theresulting Ds

tvalues, corresponding to the coefficients in the equation, are


Table 1Saving rate equation: simulated effects and estimates (t-statistics in parentheses)

Simulation EstimationVariable (1) (2) (3)

*g$%& !0.64 !1.02 (8.87) !1.05 (10.1)*gc !0.64 !0.35 (0.71) !0.56 (1.20)*v 0.82 !0.10 (0.43) !0.18 (0.91)*qy !0.31 !0.24 (1.98) !0.29 (2.40)*qc 0.34 0.17 (1.39) 0.17 (1.56)*utg 0.77 1.06 (8.70) 1.07 (9.22)!*(rdg

~1) 0.82 1.01 (1.70) 1.05 (1.54)

!*(rbg~1

) 0.66 !0.22 (0.37) !0.29 (0.54)*utp 0.88 0.77 (2.53) 0.72 (2.52)*z 0.46 0.43 (2.64) 0.24 (1.53)*(1#r)bp

~10 ! !

*k~1

0.21 0.03 (0.22) 0.05 (0.33)R2 ! 0.86 0.88AR(1) ! ! 0.50 (2.40)DW ! 1.53 1.93

computed. This computation takes into account the serial correlation of eachvariable, and the ensuing changes in the future income-tax rate. Note thatsetting the economy at the steady state in period t!1 reflects the assumptionthat the linearization of the saving rate equation (2.11) is taken at the steadystate.

The results of the simulations are shown in Table 1, column 1. To facilitatethe discussion of the results, the variables are grouped as follows: (a) governmentspending variables, (b) tax rates, (c) non-fiscal variables. Unilateral transfers tothe government from abroad are included in the first group since they amount tonegative spending.

4.3.1. Government spending variables

f g13,!rbg~1

: Although there is no empirical counterpart to g13, the simulationis carried out as a useful benchmark for the following discussion. A perma-nent increase in government spending affects national saving in three differentways. The first can be referred to as the direct/wealth effect, which takes placeeven without capital accumulation or distortionary taxation.12 Without the

12 In other words, this is the effect that would take place in a simpler model without capital in theproduction function and with lump-sump taxation.


latter two features of the model, the direct negative effect of g13 on nationalsaving is fully and immediately offset by the wealth effect on consumption andon labour effort, leaving national saving unchanged. The second is the capitalaccumulation effect. In the presence of capital accumulation, the higher laboureffort resulting from the decline in wealth induces higher current investment— given complementarity between capital and labour. Because current invest-ment affects production only in the next period, output in the future is higherthan in the present, causing a decline in the saving rate. The third is thedistortionary taxation effect, which works in the opposite direction. Giventhat current qy

tis held constant (as in the regression), the intertemporal budget

constraint of the government implies that permanently higher spendingshould be accompanied by a future increase in the income-tax rate. Thisexpectation reduces the motivation to work in the future and to invest in thecurrent period — both of which reduce future income. Hence, current income isrelatively high, inducing an increase in current savings. Interest payments onthe foreign debt, !rbg

~1, play a role similar to permanent government

expenditures, and, hence, the simulated coefficient is the same. As column 1 inTable 1 shows, the third effect is dominant (the simulated coefficient is 0.66).

f v,!rdg~1

: Transfers payments to the public affect saving only through thethird channel described above, i.e., the distortionary taxation effect. Hence,the simulated coefficient is positive (0.82), and higher than that of g13 (0.66)because it is not partially offset by the capital accumulation effect. A redis-tributive effect of transfers, as suggested by Feldstein (1982), is that thereceiving sector may be cash constrained, and hence total consumption mayincrease. This consideration, not present in the model, would generate a nega-tive coefficient. Interest payments on the internal debt, !rdg

~1, have a similar

effect as transfers and therefore the coefficient is the same.f g53,utg: All three factors described above for g13 are at work here as well.

However, in the present case the direct/wealth effect on saving is negative,because spending is temporary and thus the offsetting wealth effect on savingis weaker than for g13. The temporary nature of the change in spending alsoimplies that the other two effects are weaker than for g13: the smaller wealtheffect implies that labour effort responds more moderately — and thus thecapital accumulation effect is weaker, and the income-tax rate adjustment isexpected to be smaller — implying a weaker distortionary taxation effect.Unilateral transfers from abroad, utg, work like temporary spending, but inthe opposite direction.13

13The small difference in the magnitude of the two coefficients is related to the serial correlationcoefficients of g53 and utg, !0.64 and 0.77, correspondingly. Hence, changes in utg are moretemporary, and thus the wealth effect is weaker.


4.3.2. Tax rates

f qy: An increase in the current income-tax rate (a positive gt) generates expecta-

tions of a slightly lower tax rate starting from t#1. The currently higher taxrate motivates a decline in labour at time t, and the ensuing future tax declinehas a small but positive effect on future labour. Accordingly, current income isrelatively low, and hence the effect of income-tax rate on saving is negative:the resulting coefficient is !0.31.

f qc: An increase in the consumption-tax rate implies a temporarily high pricefor current consumption, leading to higher saving.14

4.3.3. Non-fiscal variablesDistortionary taxation has minor implications for changes in variables that

do not enter directly in the government budget constraint. The reason is that theensuing changes in output affect both government expenditures (except interestpayments, which are predetermined) and income proportionally — because theirshares in output are held constant in the simulation of the partial effects.

f z, k~1

: The productivity shock, being persistent but not permanent (autocor-relation coefficient of 0.91) has a positive effect on saving, reflecting temporar-ily high income.15 This effect is accompanied by the positive response oflabour effort to higher marginal labour productivity. The capital stock hasa similar type of effect: when it is high it adjusts gradually to the steady statelevel, generating the same type of temporarily high income and marginallabour productivity. For both variables, there is a partly offsetting incomeeffect on consumption. The resulting coefficients are 0.46 for z and 0.21for k

~1.

f utp: Transfers from abroad to the private sector have a similar effect astransfers to the public sector. The main effect is one of temporary income,which increase savings.

f bp~1

: Private foreign assets have a minor effect on savings via the income effecton labour effort. The income effect induces less labour and thus less currentinvestment, which reduces future income. The positive effect on savings is verysmall because what matters for this effect is r times the change in bp

~1.

14Given the intertemporal budget constraint of the government, a currently higher qctgenerates

expectations of lower qyt

in the future, which increase future labour and output and thus reducecurrent saving. Hence, this channel works in the opposite direction to that referred to in the text.However, given that the change in qc

tis temporary, the expected future tax reduction and the ensuing

negative effect on saving are small.

15Finn (1990) annalizes together this effect and that on investment, in the context of thecorrelation between saving and investment in a small open economy.


5. Empirical results

Columns 2 and 3 in Table 1 display the estimated coefficients (t-statistics inparentheses) to be compared with the simulated values in column 1. Note incolumn 2, which reports OLS results, the DW statistic of 1.53. Hence, even infirst differences there is some evidence of positive serial correlation in *e

t,

strongly suggesting that etis not stationary. Therefore, we can conclude now

that estimation of the savings equation in levels would not be appropriate.Column 3 reports results when an AR(1) term is included. Overall, the estimatedmodel resembles the simulated model. In particular, the estimated coefficient ofthe income-tax rate, qy, is negative and statistically significant. The privateforeign assets variable was deleted, given the negligible coefficient predicted.When included, this variable yields a t-statistic of only 0.16.

The coefficients of g$%& (!1.02 and !1.05 in columns 2 and 3, respectively)are lower than the expected value, and even lower than !1. Two possibleexplanations for this result are the following. First, an increase in militaryspending may signal good news about the future, such as the removal of anexternal threat or an increased inflow of financial assistance from abroad. Theseexpectations would trigger higher private consumption. An alternative explana-tion is that higher military spending is a reaction to the creation of a newexternal threat, which is not fully neutralized. Hence, g$%& may accompany badfuture prospects, such as higher personal risk and the possible shortening of theprivate planning horizon, inducing a depletion of private assets. Of these twoexplanations, it seems to us that the second may have some relevance in thepresent case, given Israel’s quick military reactions to external threats.

The difference in size between the coefficients of g$%& (!1.02,!1.05) andgc (!0.35,!0.56) may also be related to the fact that civilian spending isa closer substitute for private consumption than military spending. Hence, whengc increases, private consumption declines by more than when g$%& rises, result-ing in relatively less national dissaving.16

The consumption tax variable, qc, has positive coefficients, as expected, butthey are not significantly different from zero at standard significance levels(t-statistics of 1.39 and 1.56). The transfers variable v has negative but very smalland insignificant coefficients, compared to the positive and large coefficientexpected. A possible explanation for the sign and lack of significance may be the

16Corbo and Schmidt-Hebbel (1991) use panel data on developing countries and find, as we do,that increasing government spending has a stronger (negative) effect on national saving thanincreasing taxes. However, they find a positive effect of taxation, in the 0.35, 0.52 range, while herethe results indicate a negative effect.


offsetting distributional effect mentioned in Section 4: transfers benefit indi-viduals who are likely to be cash-constrained, thus increasing overall consump-tion and reducing saving.

Unilateral transfers from abroad to the public sector, utg, have the expectednegative coefficients, but they are too high (1.06,1.07), similarly as defensespending but in the opposite direction.

The coefficients of interest payments on the internal debt, !rdg~1

are, aspredicted, positive and large (1.01,1.05), but with relatively low t-statistics of 1.7and 1.5. A problem with the model’s interpretation of the positive coefficient— that it is due to expectations of a future tax increase — is the lack of significanceof interest payments on the foreign public debt, !rbg

~1. The latter variable was

also predicted to have a positive coefficient, although smaller, for the samereason.17

Unilateral transfers from abroad to the private sector utp, and the producti-vity shock z, have positive and significant coefficients, as predicted, but thet-statistic of z in column 3 is only 1.5. Finally, the capital stock has very small— 0.03, 0.05 — and insignificant coefficients, compared to the 0.21 valueexpected.18

6. Conclusions

This paper developed a procedure for interpreting the coefficients of fiscalvariables in a saving rate equation, given a rule for distortionary-tax adjustment.The rule adopted in the model is income-tax smoothing subject to a white noiseerror. This procedure is not specific to a saving rate equation; it can be appliedto the analysis of the effects of fiscal policies on any other macroeconomicvariable.

17To test whether the low significance levels of some variables is due to multicollinearity, thetheoretical restrictions that the coefficients of v and rdg

~1are the same, and that the coefficients of

g$%& and gc are the same, were imposed. In general, the results remain similar, indicating thatmulticollinearity seems not to be a problem.

18Lavi (1995) finds, using Israeli data, a positive and significant correlation between the share ofwages in national income and total consumption, and suggests that this may be due to liquidityconstraints faced by wage earners. When the ratio of wage payments to national income is added tothe equation, the coefficient on the consumption tax increases in size and in statistical significance,while the t-statistic of the income-tax rate becomes !0.9. The rest of the results are qualitativelysimilar to those in Table 1. The coefficient on the wage share is negative and significant, agreeingwith the results in Lavi. However, the wage share effect is difficult to interpret in a structural way,unless one is willing to assume that the production function parameter a shifts exogenously overtime.


The empirical results obtained from Israeli data are mixed. An interestingempirical result is the negative partial effect of the income-tax rate, as predictedby the model. This stands in contrast with the Keynesian framework, in whichhigher income taxes are expected to generate a positive comovement betweenthe income-tax rate and the national saving rate. The interpretation of thenegative effect is that, given the values of the other fiscal variables, a higherincome tax in the current period signals a lower tax rate in the future owing tothe intertemporal budget constraint. Hence, current labour and income are lowrelative to the future, and thus consumption smoothing implies a decline insaving.

Defence spending has a strong negative effect, and unilateral transfers to thepublic sector have a strong positive effect, both larger than predicted. Speculat-ive explanations have been advanced regarding defense spending, but theseresults remain unexplained. It may be interesting to explore the joint determina-tion of defense spending and unilateral transfers to the public sector, whichincreased during the war years, particularly in and after 1973.

The consumption tax rate has a positive effect on saving, as one may expectfor temporary changes in the relative price of consumption. However, thecoefficients are not statistically significant at standard significance levels. Never-theless, the results provide some evidence that a temporary shift in taxation fromincome to consumption increases the saving rate, at least as a result of thereduction in income taxation.

Acknowledgements

We thank a referee of this Journal for many helpful comments.

References

Aschauer, D.A., Greenwood, J., 1985. Macroeconomic effects of fiscal policy. Carnegie-RochesterConference Series on Public Policy 23, 91—138.

Barro, R.J., 1979. On the determination of the public debt. Journal of Political Economy 87,946—971.

Boskin, M.J., Kotlikoff, L.J., 1985. Public debt and United States saving: A new test of the neutralityhypothesis. Carnegie-Rochester Conference Series on Public Policy 23, 55—86.

Dotsey, M., 1994. Some unpleasant supply side arithmetic. Journal of Monetary Economics 33,507—524.

Corbo, V., Schmidt-Hebbel, K., 1991. Public policies and saving in developing countries. Journal ofDevelopment Economics 36, 89—115.

Feldstein, M., 1982. Government deficits and aggregate demand. Journal of Monetary Economics 9,1—20.

Finn, M., 1990. On savings and investment dynamics in a small open economy. Journal ofInternational Economics 29, 1—21.


Kotlikoff, L.J., 1984. Taxation and savings: A neoclassical perspective. Journal of EconomicLiterature XXII, 1576—1629.

Lavi, Y., 1995. Do Changes in Current Income Affect Consumption in Israel? An Empirical Test ofthe Permanent Income Hypothesis under Rational Expectations. Bank of Israel, Working Paper95.05 (Hebrew).

Seater, J.J., 1993. Ricardian equivalence. Journal of Economic Literature XXXI, 142—190.


Fiscal policy and saving under distortionary taxation

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