This paper analyses the consequences of productive government spending on private consumption. In a related work, Linnemann and Schabert (2006) found that a moderate output elasticity of government expenditures is sufficient to generate a positive consumption response to a fiscal shock. It is shown in this paper that pessimism as to the ability of productive government spending to account for an empirically observed positive consumption response is in order because a balanced budget increase in government spending increases private consumption only if the productivity of government spending is relatively high. For realistic values of the output elasticity of government spending, a positive consumption response is ruled out.

Juha Tervala

English

Research Papers in Economics

     
 
 
  
  
Volume 29, Issue 1 
  
Productive government spending and private consumption: a pessimistic view 
  
 
 
Juha Tervala  
University of Helsinki 
Abstract 
This paper analyses the consequences of productive government spending on private consumption. In a related work, 
Linnemann and Schabert (2006) found that a moderate output elasticity of government expenditures is sufficient to 
generate a positive consumption response to a fiscal shock. It is shown in this paper that pessimism as to the ability of 
productive government spending to account for an empirically observed positive consumption response is in order 
because a balanced budget increase in government spending increases private consumption only if the productivity of 
government spending is relatively high. For realistic values of the output elasticity of government spending, a positive 
consumption response is ruled out.
I wish to express my gratitude to Essi Eerola, Pertti Haaparanta and Tapio Palokangas for their comments. 
Citation: Juha Tervala, (2009) ''Productive government spending and private consumption: a pessimistic view'', Economics Bulletin, Vol. 29 
no.1 pp. 416-425. 
Submitted: Dec 18 2008.   Published: March 24, 2009. 
 
     1. Introduction
Blanchard and Perotti (2002) have studied the eﬀects of ﬁscal expansions
on output and private consumption using a structural VAR/event study ap-
proach. They found that government spending shocks have a positive eﬀect
on private consumption, which is at odds with most microfounded general
equilibrium models. Much of the recent studies (Canzoneri et al. 2003, Gali
et al. 2007, Perotti 2005) have been in agreement with this ﬁnding. On the
other hand, Mountford and Uhlig (2008) ﬁnd that a balanced budget (deﬁcit
ﬁnanced) increase in government spending decreases (increases) private con-
sumption in the short run.
A recent strand of the ﬁscal policy literature has focused on explaining
why private consumption increases after a government spending shock. Ravn
et al. (2006) developed a model where countercyclical mark-ups caused by
"deep habits" over individual varieties of consumption goods imply that pri-
vate consumption increases following a government spending shock. Ganelli
(2007) shows that demographic dynamics and ﬁnite horizons can explain
t h ep o s i t i v ep r i v a t ec o n s u m p t i o nr e s p o n s e . G a l ia ta l . ( 2 0 0 7 )h a v es h o w n
that the presence of “rule-of-thumb” consumers, who do not borrow or save,
and nominal rigidities can account for this positive private consumption re-
sponse. Ganelli and Tervala (2009), Linnemann and Schabert (2004), Rebei
and Bouakez (2007) have shown that if government spending is a complement
of private consumption, a rise in government spending can increase private
consumption.
Linnemann and Schabert (2006) developed a model in which the ﬂow of
government spending aﬀects the productivity of private ﬁrms. This implies
that a rise in government spending is similar to a technology shock that
increases the productivity of ﬁrms. They conclude that a moderate output
elasticity of government spending is suﬃcient to generate a positive private
consumption response to a balanced budget increase in government spending.
The results of this paper incline me to say that pessimism as to the ability
of productive government spending to account for the observed positive pri-
vate consumption is in order. The model presented here demonstrates that
the private consumption response to a ﬁscal shock depends on the Frisch
elasticity of labour supply and the productivity of public services. The title
of the paper includes the words "a pessimistic view" inasmuch as the results
show that for the realistic parameter combinations of the Frisch elasticity of
labour supply and the productivity of public services, a positive consumption
response to a balanced budget increase in government spending is ruled out.
The paper is structured as follows. Section Two lays out a minimal model.
Section Three analyses the implications of productive government spending
1on private consumption and output. Finally, Section Four concludes the
paper.
2. Model
2.1 Households
In this section I develop an extremely simple model to analyse the con-
sequences of productive government spending on private consumption. Con-
sider an economy with a large number of identical households and ﬁrms. The
utility function of the household is
U(C,N)=l o gC −
N1+ϕ
1+ϕ
, (1)
where C denotes private consumption of the only commodity in the economy
and N is the labour supply. Parameter ϕ measures both the elasticity of the
marginal disutility of labour with respect to labour supply and the Frisch
elasticity of labour supply,1 w h i c hi sh e r eg i v e nb y1/ϕ.
The budget constraint of the household is
PC = WN− Pτ+ π, (2)
where P is the price of the consumption commodity, w is the nominal wage
rate, τ denotes per-capita lump-sum taxes (in real terms) and π denotes the
proﬁts of the ﬁrm that the household owns (the proﬁts are, however, zero).
The household solves a maximization problem, choosing the levels of con-
sumption and leisure that maximize utility. That is, it maximizes the utility
function (1) subject to the budget constraint (2). The resulting labour supply
equation is
N
ϕ =
W
PC
. (3)
This equation simply states that the labour supply depends on the Frisch
elasticity, the real wage and private consumption.
2.2 Government and ﬁrms
The government runs a balanced budget and thus τ = G,w h e r eG denotes
per-capita government spending. Aggregate demand in the economy is given
by
Y = C + G. (4)
1The Frisch elasticity of labour supply is deﬁned as the elasticity of the labour supply
with respect to wages holding the marginal utility of consumption constant.
2The production function of the ﬁrm is
Y = NG
α, (5)
where α (α ≤ 0) measures the productivity of government spending. As
in Linnemann and Schabert (2006) I assume that the ﬂow of government
spending aﬀects the production function.
The ﬁrm maximizes proﬁts (taking the price and the wage as given)
max
N
π = PY − WN
= PNG
α − WN.
The result is
P =
W
Gα, (6)
i.e., the price is equated to the marginal cost.
3. Government spending and private consumption
3.1 Solving for the model
To keep the model and the solution as simple as possible, I log-linearize
the model around a zero government spending steady state. Since the publi-
cation of the General Theory by Keynes (1936), many economists have em-
phasized the role of sticky wages in understanding business cycles. I follow
this tradition and assume sticky wages here.2
The four equations that determine the four variables (N,C,Y,P)a r el o g -
linearized versions of (3), (4), (5) and (6):
ϕ ˆ N = − ˆ P − ˆ C, (7)
ˆ Y = ˆ C + ˆ G, (8)
ˆ Y = ˆ N − α ˆ G, (9)
ˆ P = −α ˆ G. (10)
Here percentage deviations from the initial steady state are denoted by hats:
ˆ N = dN/N0, where the zero subscript denotes the initial steady state. Since
initial government spending is zero, it is normalized by private consumption
( ˆ G = dG/C0).3
2It is useful to note that an increase in government spending tends to increase labour
supply, which in turn depresses real wages under ﬂexible wages. However since wages are
sticky, the household is better oﬀ in the case of sticky wages, and the combination of sticky
wages and perfect competition in the labour market is not problematic.
3To have a well-speciﬁed initial steady state, I assume that the production function in
the initial steady state in Y0 = N0.
33.2 Results
To determine the eﬀect of government spending on private consumption,
equations (8) and (7), solved for ˆ N, are inserted into (9) to obtain
ˆ C + ˆ G = −
1
ϕ
ˆ C −
1
ϕ
ˆ P + α ˆ G. (11)
Then inserting equation (10) into (11) and rearranging we get
ˆ C =
µ
α + αϕ − ϕ
ϕ +1
¶
ˆ G. (12)
This equation shows that a rise in government spending can increase or de-
crease private consumption depending on the productivity of government
spending (α) and the labour disutility parameter (ϕ). As emphasized by
Linnemann and Schabert (2006), when government spending is productive,
increasing it tends to (i) increase aggregate demand and (ii) raise aggregate
production. In this model, the strength of the former eﬀe c ti sc a p t u r eb yϕ,
as it governs the willingness of the household to supply more labour following
a rise in aggregate demand. The strength of the latter eﬀect is captured by
α. The higher α is, the more government spending increases the productivity
of ﬁrms.
Figure 1 on page 9 illustrates the dependence of the private consumption
response on the interplay between ϕ and α. For parameter combinations that
are along the grey line, private consumption does not change following a rise
in government spending. Above (below) the grey line a rise in government
spending increases (decreases) private consumption. For instance, if ϕ =1 ,
private consumption increases if α is greater than 0.5.
Using numerical simulations, Linnemann and Schabert (2006, 37-38) show
that if ϕ = α =0 , then a rise in government spending does not aﬀect private
consumption. But if α>0 and ϕ =0 , then a rise in government spending
increases private consumption. Equation (12) and Figure 1 illustrate the
same results: if ϕ = α =0 , then a positive shock to ˆ G does not aﬀect private
consumption. In addition, if α>0 and ϕ =0 , equation (12) becomes
ˆ C = α ˆ G. This equation and Figure 1 show that any output elasticity of
government spending can cause a rise in government spending to increase
private consumption, if the labour supply elasticity is inﬁnite (ϕ =0 ).
The question I would like to ask is whether productive government can
e x p l a i nt h eo b s e r v e dp o s i t i v ee ﬀect of government spending on private con-
sumption under plausible parameterization. In summarizing the main results
of their paper, Linnemann and Schabert (2006, 31) write that "a moderate
4production elasticity of government expenditures is suﬃcient, in a model with
lump-sum taxes, to generate eﬀects that are qualitatively consistent with the
empirically observed pattern of [a] positive [...] consumption response[s] to
a ﬁscal shock" [italics added]. Figure 1, however, demonstrates that gov-
ernment spending increases private consumption only if the productivity of
government spending is relatively high.
Empirical estimates on the output elasticity of current government spend-
ing are very few.4 Evans and Karras (1994, 1) found "fairly strong evidence
that current government educational services are productive but no evidence
that other government activities considered are productive". Their results
suggest that the output elasticity of current government educational services
is about 0.04.
Empirical estimates on the Frisch elasticity of labour supply (given by
1/ϕ in this model) are more numerous. However, these do not seem to
be conclusive as to what a plausible value for the Frisch elasticity is. In
his Nobel Lecture, Prescott (2006, 226) argued that the Frisch elasticity of
labour supply is 3 in the United States. If ϕ =1 /3, then a rise in government
spending increases private consumption only if α>0.25.
Domeij and Floden (2006) brieﬂy surveyed the Frisch elasticity estimates
from microdata. They found that most estimates are in the range of 0 and
0.5. However, they argued that these estimates may be downward biased up
to 50 percent. Thus, if the true Frisch elasticity of labour supply is 1, the
econometrician would ﬁnd a value of 0.5. Assuming that the Frisch elasticity
is 0.5 (ϕ =2 ), the productivity of current government spending needs to
be 0.67 for a rise in government spending to increase private consumption,
according to this model.
Some estimates suggest that the Frisch elasticity of labour supply is higher
than 0.5. For instance, Kimball and Shapiro (2008) found that the Frisch
elasticity of labour supply is about 1. Figure 1 shows that if ϕ =1 ,ar i s ei n
government spending increases private consumption when α>0.5.
The empirical estimates of the productivity of current government spend-
ing and the Frisch elasticity of labour supply suggest that pessimism as to
the ability of productive government spending to account for a positive con-
sumption response is in order. This is because a rise in government spending
increases private consumption only if the productivity of government spend-
ing is relatively high, and for realistic parameter combinations of α and ϕ,a
positive consumption response is ruled out.
4Virtually all empirical papers that estimate the productivity of public services focus
on estimating the productivity of public capital, not current (the ﬂow of) government
spending.
53.3 Fiscal policy multiplier
Finally, although a rise in government spending — in this model — does not
necessarily increase private consumption, this does not imply that productive
government spending is useless. The most easily this can be seen is by
inserting equation (12) into (8) to yield the ﬁscal multiplier
ˆ Y =
µ
α + αϕ +1
ϕ +1
¶
ˆ G. (13)
This equation shows that the ﬁscal multiplier is increasing in α.I ft h eg o v -
ernment in a recession would like to increase output, it would be better to
use government spending on education, for example, rather than for non-
productive purposes.
4. Conclusions
Recent empirical evidence suggests that a rise in government spending
can have a positive eﬀect on private consumption. The main objective of
this paper is to answer the question of whether a rise in productive govern-
ment spending can account for an empirically observed positive consumption
response. Consistent with Linnemann and Schabert (2006), I ﬁnd that if
the productivity of public services is suﬃciently high, a balanced budget
rise in government spending can increase private consumption. The model
presented in this paper shows that the impact of a ﬁscal shock on private
consumption depends greatly on the Frisch elasticity of labour supply and
the productivity of public services. It is argued that — in the context of this
model — under plausible parameterization, a positive consumption response
is ruled out. Finally, I would like to emphasize that there is no reason to
downplay the signiﬁcance of productive government spending. This is be-
c a u s ep r o d u c t i v eg o v e r n m e n ts p e n d i n gi sm o r ee ﬀective than non-productive
spending in terms of inﬂuencing the country’s output. However, a rise in
productive government spending is unlikely to have an eﬀect strong enough
on output that private consumption would increase.
6References
[1] Blanchard, O and R. Perotti (2002) "An Empirical Characterization of
the Dynamic Eﬀects of Changes in Government Spending and Taxes on
Output" Quarterly Journal of Economics 177, 1329—1368.
[2] Canzoneri, M., R. Cumby and B. Diba (2003) "New Views on the
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[3] Domeij, D and M. Floden (2006) "The Labor-Supply Elasticity and Bor-
rowing Constraints: Why Estimates Are Biased" Review of Economic
Dynamics 9,2 4 2 - 2 6 2 .
[4] Evans, P and G. Karras (1994) "Are Government Activities Produc-
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[13] Perotti, Roberto (2005) "Estimating the Eﬀects of Fiscal Policy in
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[15] Ravn, M., S. Schmitt-Grohe and M. Uribe (2006) "Deep Habits" Review
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40,9 5 4 - 9 7 9 .
8Figure 1: The dependence of private consumption response on the interplay
between α and ϕ
0 0.25 0.5 0.75 1 1.25 1.5
Value of ϕ
0
0.1
0.2
0.3
0.4
0.5
0.6
e
u
l
a
V
f
o
α
9

Productive government spending and private consumption: a pessimistic view

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