This paper considers a simple model in which government spending is productive and has a complementary relationship with private consumption to study the response of the latter to government spending. We discuss how these two characteristics can yield empirical observations that indicate a positive re sponse of private consumption to government spending. By assuming some plausible parameter settings, we demonstrate that these dual aspects of government spending, which are normally treated separately in the literature, are inseparably linked. Our findings reveal that in addition to the presence of complementarity, productivity—even if minimal—increases the likelihood of generating a positive consumption response.
Canonical models in modern macroeconomics predict the negative response of private consumption to government spending owing to a negative wealth effect (e.g., Aiyagari et al. [
Multiple hypotheses have been advanced to bridge the gap between theory and empirical evidence for explaining the positive response of consumption to government spending. Among these, there are two prominent hypotheses regarding characteristics of government spending.
On the one hand, some predecessors look at the demand side and focus on the complementarity between government spending and private consumption by applying Bailey’s [
Additionally, the production elasticity of government spending is also a significant consideration in studying the impact of government expenditure on production. In this context, empirical works project mixed estimates. At 40 percent, Aschauer [
This paper works in the direction of showing that the dual aspects of public expenditure, which are normally treated separately in the literature, are inseparably linked under some plausible parameter settings. This has been achieved by combining the standpoints of Ganelli and Tervala [
The rest of the paper is organized as follows. The model has been described in Section 2 and results have been presented and discussed in Section 3. Section 4 concludes.
We consider a model economy in which the foregoing dual aspects of government spending (i.e., productivity and complementarity) are incorporated. As mentioned in detail below, productivity pertains to production function and complementarity to utility function.
In the literature, Linnemann and Schabert [
Y = N G α (1)
where Y is output level, N is labor input, G is government spending, and α ( ≥ 0 ) is the production elasticity of government spending. Let P and W denote the price and wage, respectively. The profits are given by the following expression:
π = P Y − W N
and maximization with respect to N results in the following:
P = W G α (2)
We now turn to household behavior. There is a representative household that seeks to maximize the utility function, with which the possible complementarity between government spending and private consumption is incorporated. Specifically, as in Ganelli and Tervala [
U = ln ( C + ψ G ) − N 1 + ϕ 1 + ϕ
where C is private consumption, N is labor supply, and ϕ ( ≥ 0 ) is the elasticity of the marginal disutility of labor supply. Following Tervala [
Noting that the profits of the firm are zero, the budget constraint is
P C = W N − P τ
where τ denotes real lump-sum taxes to which the government has access, and the government spending is financed entirely by τ in a balanced budget, such that τ = G . Utility maximization with respect to C and N yields the following:
1 C + ψ G = P N ϕ W (3)
We now log-linearize the model as in Ganelli and Tervala [
Y ^ = N ^ + α G ^ (4)
P ^ = − α G ^ (5)
C ^ + ψ G ^ = − ϕ N ^ − P ^ (6)
Y ^ = C ^ + G ^ (7)
where hats refer to percentage deviations from the initial steady state.
This section focuses on both productivity and complementarity of government spending and examines how these two characteristics can yield empirical observations, especially with regard to the response of private consumption to government spending.
The main indications of the present model can be inferred from the above Equations (4)-(7). By solving the equations for C ^ and Y ^ as a function of G ^ , we obtain C ^ = m C G ^ and Y ^ = m Y G ^ , where
m C ≡ α + α ϕ − ϕ − ψ 1 + ϕ (8)
m Y ≡ α + α ϕ − ψ + 1 1 + ϕ (9)
which are the same as the results of Tervala [
These two equations imply that the impact of government spending on private consumption and output is determined by three parameters: α , ϕ , and ψ . First, as is clear from (7), m Y is larger than m C and they differ by one: m Y − m C = 1 . Moreover, the marginal changes of m Y and m C are equivalent, such that
μ α ≡ ∂ m C ∂ α = ∂ m Y ∂ α = 1
μ ψ ≡ ∂ m C ∂ ψ = ∂ m Y ∂ ψ = − 1 1 + ϕ
μ ϕ ≡ ∂ m C ∂ ϕ = ∂ m Y ∂ ϕ = ψ − 1 ( 1 + ϕ ) 2
As detailed in subsequent subsection, since we consider the case where ϕ ≥ 0 and ψ ∈ [ − 2,1 ] , it follows that μ ψ is negative and μ ϕ is equal to or lower than zero. Our main interest is in assessing the effects of α and ψ on the two multipliers. Evidently, as emphasized in previous works, both parameters play an important role. First, without relying on any parameters, the multipliers are linear-proportional to α . This implies that the productivity of government spending can not only positively enhance the response of output, but also private consumption, to a rise in government spending, as shown in Linnemann and Schabert [
Up to this point, we have given a simple quantitative rating of the government spending multipliers. In what follows, we focus primarily on the qualitative aspect. For investigating whether or not private consumption and output respond positively to a rise in government spending, we only have to observe their sign.
From an aforementioned condition ( ϕ ≥ 0 ), (8) and (9), we readily obtain the following propositions.
Proposition 1. Government spending leads to a rise in private consumption if and only if
m C > 0 ⇔ α + α ϕ − ϕ − ψ > 0 .
Proposition 2. Government spending leads to a rise in output if and only if
m Y > 0 ⇔ α + α ϕ − ψ + 1 > 0 .
Proposition 1 asserts that private consumption can respond positively to a rise in government spending only when α is large or ψ is small, or both are satisfied. On the contrary, Proposition 2 suggests that the positive output response requires easier conditions.
We further explore how the government spending multipliers can be positive within some realistic parameter settings. Before considering possible parameter settings, we provide an overview of the estimates in previous empirical works, which are relevant to the following exploration.
There are three key parameters for determining the sign of government spending multipliers as shown in (8) and (9). We review the estimates of α and ϕ according to Tervala [
The second parameter is the Frisch elasticity of labor supply, denoted earlier by 1 / ϕ . Till date, many empirical studies have attempted to estimate this value (e.g., MaCurdy [
The third parameter is ψ . While Ganelli and Tervala [
Summarizing the above-mentioned empirical evidence, it seems reasonable to assume that approximately, α is minimal, ϕ = 1 , and ψ = − 1 . In what follows, these are taken into account.
an increase (decrease) in private consumption. For comparison with Tervala [
We begin by reconfirming the case of Tervala [
Next, we consider the case of Ganelli and Tervala [
In summary, it is shown that neither productivity nor complementarity can solely generate positive consumption response in the present model based on Tervala [
For simplicity, we again assume the plausible case that government spending is a perfect complement to private consumption ( ψ = − 1 ) and the Frisch elasticity of labor supply is equal to one ( ϕ = 1 ). Additionally, mildly productive government spending is introduced, and we assume that α runs from higher than 0 through 0.4 at most. Given such parameter settings, there is a definite possibility of the presence of ( ϕ , α , ψ ) in the space below the threshold surface in
Incidentally, mildly productive government spending may have relevance to the positive output response. Similar to
This paper took particular note of a critical gap between theory and empirical evidence in macroeconomics and proposed some new implications. It dealt with the dual aspects of government spending, which are normally treated separately in the literature, and demonstrated that they are inseparably linked. In this context, reconciliation of the empirical evidence that private consumption positively responds to a rise in government spending is necessary. Some plausible parameter settings are considered in this study, and unlike Linnemann and Schabert [
Moreover, mildly productive government spending can be crucial for explaining the empirical observation. Once an appreciable extent of complementarity is assumed, the empirical observation can be explained by productivity, even if it takes some minimal values. In contrast to private consumption, the output in general is likely to respond positively to a rise in government spending only in the presence of mild productivity.
Policymakers are prone to increase government expenditures during an economic turndown. However, from a welfare perspective, not only output but also consumption is relevant. Our results suggest that policymakers need to recognize the importance of quality of government spending rather than quantity when stimulating an economy without a decline in consumption.
The author thanks an anonymous referee and Hiroshi Ohta for the helpful comments. Financial support from Grants-in-Aid for Scientific Research (C) (25380368, 17K03770) is gratefully acknowledged.
Funashima, Y. (2017) A Comprehensive Analysis of the Response of Private Consumption to Government Spending. Theoretical Economics Letters, 7, 1965-1974. https://doi.org/10.4236/tel.2017.77133