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Fiscal policy with direct effects
Economics Letters 5 (1980) 219-224 0 North-Holland Publishing Company
FISCAL POLICY WiTH DIRECT EFFECTS *
Nicolaas GROENEWOLD Universitv of’ Tasrmnia, Received
5 September
Tasmania
7001, Australia
1980
This paper analyses the effects of fiscal policy in a model where government expenditure and tax changes affect household behaviour directly. This is shown to have implications for both the macroeconomic and welfare effects of changes in government spending.
1. Introduction
This paper analyses the effects of fiscal policy within the framework of a singleperiod model. The macro model used is based on the maximising behaviour of the representative household and the representative firm and takes into account the direct effects of government expenditure changes on household behaviour and of taxes on labour supply. The central conclusions of the paper are first, that from a macroeconomic point of view, an expansion of government expenditure does not necessarily increase output even in a fixed-price, excess-supply situation. Furthermore, even if output rises, the utility of the representative household may not be improved. Secondly, from the point of view of Public Finance, setting the level of govermnent expenditure to ensure that the MRT = MRS does not maximise welfare even if the distortionary effects of taxes are ignored.
2. The model Consider an economy composed of households, firms and a government. There is a single commodity which firms produce using only labour services and which house* This is an abbreviated
and somewhat simplified version of part of my Ph. D. thesis: ‘The effectiveness of fiscal policy: A theoretical analysis’ (University of Western Ontario, 1979). In the more extensive treatment there, bonds are introduced and bond-financed and moneyfinanced fiscal policies are also examined for both a single period and over time. 1 am indebted to my thesis committee of Peter Howitt, Michael Parkin and Joel Fried for their encouragement and advice. 219
220
N. Groenewold /Fiscal policy with direct effects
holds consume and which is purchased by the government. There is a single asset, money, provided by the government and held by households. It is assumed that households and firms are price-takers and we discuss the behaviour of the representative house’hold supposing this behaviour to be typical also of the aggregate economy so that we move from the individual to the aggregate level with no change of notation [see, e.g., Howitt (1978) Barro and Grossman (1976)]. Consider the representative household first. It is assumed that government spending and tax policies affect household behaviour directly as well as indirectly and, specifically, that government expenditure is on a consumption good which it provides to households 1 (from which utility is derived) and that tax revenue is raised both by a wage tax (which affects labour-supply decisions) and by lump-sum taxes. Real money balances are included in the utility function as a measure of liquidity services [see, e.g., Sidrauski (1967), Brock (1975)] or, alternatively, since we analyse only a single-period problem, as a proxy for future consumption. Thus, the representative household maximises
where = real private consumption, = real government expenditure, M/p = real balances, ns = labour supply. c
g
The budget constraint
is
MO -M c=(l
-cY(y)wns+.+_
P
-t>
where = the average tax rate on wage income, 7r = profits distributed by firms, M,, = initial nominal balances, t = lump-sum taxes, = the real wage rate. W a
Since we wish to focus on the relationship
between c andg in household decisions,
1 A model where government expenditure directly affects household consumption behaviour is contained in Bailey (1971). However, his aggregate analysis is not motivated by the maximising behaviour of individual agents and he implicitly assumes that the MRS as well as the MRT is identically equal to unity. See also Buiter (1977) for a discussion of ‘direct crowding-out’.
N. Groenewold
/Fiscal
it is assumed that the utility function
policy
with direct effects
221
has the following special form:
LJ = u (c, g) + Z(M/P) + i(flS) , (3)
u,,ug>o>
u,,,ugg
Necessary conditions
Z”
z’>o,
for a maximum
j’,j”
may be rewritten
to give
UC(c, g) = Z’(WP) >
(4)
j’(n”)/(l
(5)
-a)
W = -z’(Mlp)
Consider, now, the representative supply of output o/“) to maximise 71= f(nd) so
-
wrP
firm. It chooses its demand for labour (nd) and
)
that
f’(nd) = w )
(6)
ys=f(rP) .
(7)
The equilibrium
conditions
are
JJ=c+g,
(8)
ns = nd
(9)
Finally, the government’s straint:
policy options are limited by the following budget con-
M-M,,
(10)
g=awn+t+p. 3. Fiscal policy
This paper considers only balanced-budget fiscal policy. Consider first the effects under fixed prices and excess supply of both commodities and labour. In that case nS will not be a household decision variable but eq. (4) will still apply, output will be determined by eq. (8) and employment by the inverse of the production function, given output. Balanced-budget fiscal policy is taken to be a change ing with M = MO, given. Then eq. (4) implies that dc/dg = -u,~/u,,
$ 0
as
ucg $ 0 .
Thus, whether expansionary fiscal policy leads to a rise in consumption the nature of the relationship between private and public consumption function. Using eq. (8) the effects on output and employment are
(11) depends on in the utility
222
N. Groenewold /Fiscal policy with direct efjrects
drl/dg = (1 /j”) dy/dg = (1 /f’)(dc/dg
+ 1) $ 0
as
+
2 u,,
Thus, if uG > 0 consumption, output and employment all increase following expansionary fiscal policy. However if uCg < 0 consumption will fall because of the direct effects of fiscal policy and the decline in private consumption may be sufficient to more than offset the increase ing. If u,~ = u,, (c andg are, in a sense, ‘perfect substitutes’) dc/dg = -1 and the decline in consumption exactly offsets the effect on aggregate demand of the increase in g, leaving output and employment unchanged. Settingj’(n) = 0 for the unemployment case, the effect of fiscal policy on the representative household’s utility (welfare) is seen to be
and this is positive ifg is a normal good. which it may be irrespective of the sign of uLg. Thus. for the fixed-price case, the following results are established: (a) A balanced-budget increase ing will not necessarily increase either consumption or output (and employment). (b) A balanced-budget increase ing may increase employment while reducing welfare and vice versa. (c) The typical optimality condition u,/u~ = 1 (MRS = MRT) implies stationarity of iJ only if u,, = uC., i e ., c and g are ‘perfect substitutes’ in the sense defined above. We will now briefly consider the effects of fiscal policy with flexible prices and full employment. The system of eqs. (4)-(9) define the equilibrium values of the endogenous variables c, y, I_‘,17’. tzd and w and may be combined to give the following three-equation system in c, II and p: &Xc, g) = Z’(M/P) a
(12)
i’(n)/z’(M/P)
(13)
= (1 - cf>f’(lZ) ,
c +g =f’(n)
(14)
The government has two tax instruments, CYand t, and we assume that the change in g is initially balanced by a change in (Yand that ‘subsequent’ changes in tax revenue brought about by changes in the real wage rate and employment are matched by changing t. Then
(15)
da = dg/womo . This considerably
simplifies the algebra compared to
dg = d(crwn) = wndoc + andw + olwdrz , and yet captures the effect of a change in (Yon labour supply. Using (15) and differentiating (12)-(14) with respect tog we have
N. Groenewold / Fiscal policy with direct efTects
dc/dg = [ucx v~‘me/z”]
+ z’nz,, [(i”/z’) + (1 - o)f”’ ~ (f”)‘/wono]]/]J]
223
,
where ]J I> 0 is the Jacobian determinant of the system (12)-(14). Given the earlier sign restrictions, the sign of dc/dg is ambiguous. It is clear, however, that dc/dg < 0 if ucg < 0. Moreover the expression can be broken up into two components:
where the first term on the right-hand side measures the change in c if only lumpsum taxes are adjusted to balance the budget and the second term, which is negative, reflects the effect of changing (Yon labour supply and hence on output and consumption. If this latter effect is ignored, it is straightforward to establish that dL
= -1
if and only if
uLX= u,., ,
Ga=z which is identical to the result established for the fixed-price regime where the assumption of excess supply of labour implied that a change in 01had no effect on output. The effect on output and equilibrium employment is given by
dy G
=
KfY‘mo/z”>(&g - u,,) - z’nhJ(f’)‘/wonol/lJI
and
Hence if the tax rate on wage income is held constant, a balanced-budget expansion of g increases real output and employment only if ucg > u,,. The effect of also increasing o( is to erode any possible increase in output. Finally, the effect on utility of the representative household is given by I Z ucg Ugt,i Z
Clearly, this expression is more complicated than that for the fixed-price case. However, if ucg = u,, and 01= q then it is again true that dU/dg = 0 if u,. = ug, i.e., the MRS (u,/uJ = MRT (1). This typical optimality condition holds, therefore, only under special circumstances. In general, we may conclude: (1) From a macro-economic point of view, it is clear that a balanced-budget fiscal policy exercise will not necessarily increase .Vand even if y increases and p falls, welfare is not necessarily increased. (2) From the point of view of public economics, it is not generally optimal to set g such that u, = ug (MRS = MRT) even if the distortionary effect of the wage tax is ignored.
224
N. Groenewold / Fiscal policy with direct effects
References Bailey, M.J., 1971, National income and the price level (McGraw-Hill, New York). Barro, R.J. and H.I. Grossman, 1976, Money, employment and inflation (Cambridge University Press, Cambridge). Brock, W.A., 1975, A simple perfect foresight monetary model, Journal of Monetary Economics 1,133-150. Buiter, W.H., 1977, ‘Crowding out’ and the effectiveness of fiscal policy, Journal of Public Economics 7, 3099328. Howitt, P.W., 1978, The limits to stability of a full-empioyment equilibrium, Scandinavian Journal of Economics 80, 2655282. Sidrauski, M., 1967, Rational choice and patterns of growth in a monetary economy, American Economic Review, Papers and Proceedings 57, 534-544.
FISCAL POLICY WiTH DIRECT EFFECTS *
Nicolaas GROENEWOLD Universitv of’ Tasrmnia, Received
5 September
Tasmania
7001, Australia
1980
This paper analyses the effects of fiscal policy in a model where government expenditure and tax changes affect household behaviour directly. This is shown to have implications for both the macroeconomic and welfare effects of changes in government spending.
1. Introduction
This paper analyses the effects of fiscal policy within the framework of a singleperiod model. The macro model used is based on the maximising behaviour of the representative household and the representative firm and takes into account the direct effects of government expenditure changes on household behaviour and of taxes on labour supply. The central conclusions of the paper are first, that from a macroeconomic point of view, an expansion of government expenditure does not necessarily increase output even in a fixed-price, excess-supply situation. Furthermore, even if output rises, the utility of the representative household may not be improved. Secondly, from the point of view of Public Finance, setting the level of govermnent expenditure to ensure that the MRT = MRS does not maximise welfare even if the distortionary effects of taxes are ignored.
2. The model Consider an economy composed of households, firms and a government. There is a single commodity which firms produce using only labour services and which house* This is an abbreviated
and somewhat simplified version of part of my Ph. D. thesis: ‘The effectiveness of fiscal policy: A theoretical analysis’ (University of Western Ontario, 1979). In the more extensive treatment there, bonds are introduced and bond-financed and moneyfinanced fiscal policies are also examined for both a single period and over time. 1 am indebted to my thesis committee of Peter Howitt, Michael Parkin and Joel Fried for their encouragement and advice. 219
220
N. Groenewold /Fiscal policy with direct effects
holds consume and which is purchased by the government. There is a single asset, money, provided by the government and held by households. It is assumed that households and firms are price-takers and we discuss the behaviour of the representative house’hold supposing this behaviour to be typical also of the aggregate economy so that we move from the individual to the aggregate level with no change of notation [see, e.g., Howitt (1978) Barro and Grossman (1976)]. Consider the representative household first. It is assumed that government spending and tax policies affect household behaviour directly as well as indirectly and, specifically, that government expenditure is on a consumption good which it provides to households 1 (from which utility is derived) and that tax revenue is raised both by a wage tax (which affects labour-supply decisions) and by lump-sum taxes. Real money balances are included in the utility function as a measure of liquidity services [see, e.g., Sidrauski (1967), Brock (1975)] or, alternatively, since we analyse only a single-period problem, as a proxy for future consumption. Thus, the representative household maximises
where = real private consumption, = real government expenditure, M/p = real balances, ns = labour supply. c
g
The budget constraint
is
MO -M c=(l
-cY(y)wns+.+_
P
-t>
where = the average tax rate on wage income, 7r = profits distributed by firms, M,, = initial nominal balances, t = lump-sum taxes, = the real wage rate. W a
Since we wish to focus on the relationship
between c andg in household decisions,
1 A model where government expenditure directly affects household consumption behaviour is contained in Bailey (1971). However, his aggregate analysis is not motivated by the maximising behaviour of individual agents and he implicitly assumes that the MRS as well as the MRT is identically equal to unity. See also Buiter (1977) for a discussion of ‘direct crowding-out’.
N. Groenewold
/Fiscal
it is assumed that the utility function
policy
with direct effects
221
has the following special form:
LJ = u (c, g) + Z(M/P) + i(flS) , (3)
u,,ug>o>
u,,,ugg
Necessary conditions
Z”
z’>o,
for a maximum
j’,j”
may be rewritten
to give
UC(c, g) = Z’(WP) >
(4)
j’(n”)/(l
(5)
-a)
W = -z’(Mlp)
Consider, now, the representative supply of output o/“) to maximise 71= f(nd) so
-
wrP
firm. It chooses its demand for labour (nd) and
)
that
f’(nd) = w )
(6)
ys=f(rP) .
(7)
The equilibrium
conditions
are
JJ=c+g,
(8)
ns = nd
(9)
Finally, the government’s straint:
policy options are limited by the following budget con-
M-M,,
(10)
g=awn+t+p. 3. Fiscal policy
This paper considers only balanced-budget fiscal policy. Consider first the effects under fixed prices and excess supply of both commodities and labour. In that case nS will not be a household decision variable but eq. (4) will still apply, output will be determined by eq. (8) and employment by the inverse of the production function, given output. Balanced-budget fiscal policy is taken to be a change ing with M = MO, given. Then eq. (4) implies that dc/dg = -u,~/u,,
$ 0
as
ucg $ 0 .
Thus, whether expansionary fiscal policy leads to a rise in consumption the nature of the relationship between private and public consumption function. Using eq. (8) the effects on output and employment are
(11) depends on in the utility
222
N. Groenewold /Fiscal policy with direct efjrects
drl/dg = (1 /j”) dy/dg = (1 /f’)(dc/dg
+ 1) $ 0
as
+
2 u,,
Thus, if uG > 0 consumption, output and employment all increase following expansionary fiscal policy. However if uCg < 0 consumption will fall because of the direct effects of fiscal policy and the decline in private consumption may be sufficient to more than offset the increase ing. If u,~ = u,, (c andg are, in a sense, ‘perfect substitutes’) dc/dg = -1 and the decline in consumption exactly offsets the effect on aggregate demand of the increase in g, leaving output and employment unchanged. Settingj’(n) = 0 for the unemployment case, the effect of fiscal policy on the representative household’s utility (welfare) is seen to be
and this is positive ifg is a normal good. which it may be irrespective of the sign of uLg. Thus. for the fixed-price case, the following results are established: (a) A balanced-budget increase ing will not necessarily increase either consumption or output (and employment). (b) A balanced-budget increase ing may increase employment while reducing welfare and vice versa. (c) The typical optimality condition u,/u~ = 1 (MRS = MRT) implies stationarity of iJ only if u,, = uC., i e ., c and g are ‘perfect substitutes’ in the sense defined above. We will now briefly consider the effects of fiscal policy with flexible prices and full employment. The system of eqs. (4)-(9) define the equilibrium values of the endogenous variables c, y, I_‘,17’. tzd and w and may be combined to give the following three-equation system in c, II and p: &Xc, g) = Z’(M/P) a
(12)
i’(n)/z’(M/P)
(13)
= (1 - cf>f’(lZ) ,
c +g =f’(n)
(14)
The government has two tax instruments, CYand t, and we assume that the change in g is initially balanced by a change in (Yand that ‘subsequent’ changes in tax revenue brought about by changes in the real wage rate and employment are matched by changing t. Then
(15)
da = dg/womo . This considerably
simplifies the algebra compared to
dg = d(crwn) = wndoc + andw + olwdrz , and yet captures the effect of a change in (Yon labour supply. Using (15) and differentiating (12)-(14) with respect tog we have
N. Groenewold / Fiscal policy with direct efTects
dc/dg = [ucx v~‘me/z”]
+ z’nz,, [(i”/z’) + (1 - o)f”’ ~ (f”)‘/wono]]/]J]
223
,
where ]J I> 0 is the Jacobian determinant of the system (12)-(14). Given the earlier sign restrictions, the sign of dc/dg is ambiguous. It is clear, however, that dc/dg < 0 if ucg < 0. Moreover the expression can be broken up into two components:
where the first term on the right-hand side measures the change in c if only lumpsum taxes are adjusted to balance the budget and the second term, which is negative, reflects the effect of changing (Yon labour supply and hence on output and consumption. If this latter effect is ignored, it is straightforward to establish that dL
= -1
if and only if
uLX= u,., ,
Ga=z which is identical to the result established for the fixed-price regime where the assumption of excess supply of labour implied that a change in 01had no effect on output. The effect on output and equilibrium employment is given by
dy G
=
KfY‘mo/z”>(&g - u,,) - z’nhJ(f’)‘/wonol/lJI
and
Hence if the tax rate on wage income is held constant, a balanced-budget expansion of g increases real output and employment only if ucg > u,,. The effect of also increasing o( is to erode any possible increase in output. Finally, the effect on utility of the representative household is given by I Z ucg Ugt,i Z
Clearly, this expression is more complicated than that for the fixed-price case. However, if ucg = u,, and 01= q then it is again true that dU/dg = 0 if u,. = ug, i.e., the MRS (u,/uJ = MRT (1). This typical optimality condition holds, therefore, only under special circumstances. In general, we may conclude: (1) From a macro-economic point of view, it is clear that a balanced-budget fiscal policy exercise will not necessarily increase .Vand even if y increases and p falls, welfare is not necessarily increased. (2) From the point of view of public economics, it is not generally optimal to set g such that u, = ug (MRS = MRT) even if the distortionary effect of the wage tax is ignored.
224
N. Groenewold / Fiscal policy with direct effects
References Bailey, M.J., 1971, National income and the price level (McGraw-Hill, New York). Barro, R.J. and H.I. Grossman, 1976, Money, employment and inflation (Cambridge University Press, Cambridge). Brock, W.A., 1975, A simple perfect foresight monetary model, Journal of Monetary Economics 1,133-150. Buiter, W.H., 1977, ‘Crowding out’ and the effectiveness of fiscal policy, Journal of Public Economics 7, 3099328. Howitt, P.W., 1978, The limits to stability of a full-empioyment equilibrium, Scandinavian Journal of Economics 80, 2655282. Sidrauski, M., 1967, Rational choice and patterns of growth in a monetary economy, American Economic Review, Papers and Proceedings 57, 534-544.