Public Spending Management and Macroeconomic Interdependence

Abstract

This paper studies the domestic and international effects of “public competition policies” aimed at improving the efficiency of public spending. Such measures are modeled as an increase in the price elasticity of public consumption. The paper finds that public competition policies significantly affect macroeconomic interdependence across countries, both through the impact of the international elasticity of substitution and of mark-up effects. The paper also develops an extension in which fiscal shocks are stochastic. In welfare terms, countries with a larger government sector have an incentive to promote global public competition policies regardless of whether fiscal policy is modeled as deterministic or stochastic.

Appendix

1.1 The initial steady-state

The numerical solutions are based on reduced forms derived from a log-linear approximation of the model around a symmetric steady state. We log-linearize the model starting from a non-zero government spending position. In order to preserve symmetry, we consider an initial steady state in which the positive level of public spending is the same in both countries and initial net foreign assets are zero in both countries. Denoting the initial pre-shock values with the subscript _SS , in such a steady state the following relationships hold: $G_{{SS}} = G^{ * }_{{SS}} = G^{W}_{{SS}} > 0$, $B_{{SS}} = B^{ * }_{{SS}} = 0$, $p_{{SS}} {\left( z \right)} = P_{{SS}} = P_{{G_{{SS}} }}$, $p^{ * }_{{SS}} {\left( z \right)} = P^{ * }_{{SS}} = P^{ * }_{{G_{{SS}} }}$, $C_{{SS}} = C^{ * }_{{SS}} = C^{W}_{{SS}}$ and $Y_{{SS}} = Y^{ * }_{{SS}} = Y^{W}_{{SS}}$. Steady state levels of the main variables are given by

$$ \delta = r_{0} = \frac{{1 - \beta }} {\beta } $$

$$ \frac{{W_{{SS}} }} {{P_{{SS}} }} = \frac{{\theta - 1 + {\left( {\eta - 1} \right)}\lambda }} {{\theta + \eta \lambda }} $$

$$ Y_{{SS}} = {\left\{ {\frac{{{\left( {1 + \lambda } \right)}{\left[ {{\left( {\theta - 1} \right)} + {\left( {\eta - 1} \right)}\lambda } \right]}}} {{k{\left( {\theta + \eta \lambda } \right)}}}} \right\}}^{{\frac{1} {2}}} $$

$$ C_{{SS}} = \frac{{Y_{{SS}} }} {{1 + \lambda }} $$

and

$$ \frac{{M_{{SS}} }} {{P_{{SS}} }} = \chi \frac{{1 + \delta }} {\delta }C_{{SS}} $$

where $\lambda = \frac{{G_{{SS}} }} {{C_{{SS}} }}$ is the ratio of public to private spending in the initial steady state.

1.2 Log-linearization

The log-linearized version of the domestic economy is presented in Table 6. Log deviations in the period in which the shock hits (the short run) are denoted by lower cases with a tilde. Lower cases with a hat denote long-run variables. The variables $\widetilde{p}{\left( h \right)}$ and $\widetilde{p}{\left( f \right)}$ denote, respectively, the short-run log-deviations of the prices set by a representative domestic and foreign firm. The hypothesis of one period pre-set prices in the producers’ currency means that we can set $\widetilde{p}{\left( h \right)} = \widetilde{p}{\left( f \right)} = 0$ in all the equations listed in Table 6 and in their analogous for the foreign economy. Since the initial steady state of net foreign assets is zero, $\widehat{b}$ is defined as $\widehat{b} = \frac{{dB}} {{C_{{SS}} }}$.

Table 6 The log-linearized domestic economy

Log-linearization around a symmetric initial steady state in which the law of one price holds implies that the log-linearized versions of the private and of the public price indexes are equivalent, as shown in equation (A1). Equations (A2) to (A10) are respectively (log linearized versions of) the world demand function for the representative differentiated good, the Euler equation, short and long-run money demand equations, the labor-leisure trade off equation, short run and long run current account equations, the optimal pricing rule (Eq. 12) and the PPP equation.

In Table 6 ψ ₁,ψ ₂ and ψ ₃ are composite parameters, which are functions of the other parameters defined as follows

$$ \begin{aligned} &\psi _{1} = \frac{{\theta - 1}} {{\theta - 1 + \lambda {\left( {\eta - 1} \right)}}} - \frac{\theta } {{\theta + \lambda \eta }},\quad \psi _{2} = \frac{{\lambda {\left( {\eta - 1} \right)}}} {{\theta - 1 + \lambda {\left( {\eta - 1} \right)}}} - \frac{{\lambda \eta }} {{\theta + \lambda \eta }}, \\ &\psi _{3} = \frac{{\theta {\left( {\theta - 1} \right)}}} {{\theta - 1 + \lambda {\left( {\eta - 1} \right)}}} - \frac{{\lambda \eta {\left( {\eta - 1} \right)}}} {{\theta - 1 + \lambda {\left( {\eta - 1} \right)}}} - \frac{{\theta ^{2} }} {{\theta + \lambda \eta }} - \frac{{\lambda \eta ^{2} }} {{\theta + \lambda \eta }} \\ \end{aligned} $$

Using the equations contained in Table 6 and the analogous expression for the foreign economy, we derived reduced forms for endogenous variables as functions of fiscal shocks and of the parameters of the model only. The reduced forms have been used to provide the numerical solutions. Given our focus on the effects of public competition policies in presence of asymmetric fiscal shocks, in our experiments we always set money shocks to zero.