Productive government expenditure and its impact on income inequality: evidence from international panel data

Abstract

This paper addresses the impact of productive government expenditure on income inequality using a dataset of 80 countries over the period of 1980–2015. It incorporates the conflicting predictions implied by alternative growth models on this issue. While the neoclassical model suggests that productive government expenditure will reduce long-run income inequality, the corresponding endogenous growth model suggests the opposite. We examine this proposition, by considering both the aggregate Gini coefficient, and the income shares of quintiles. The results obtained using the Gini coefficients provide compelling support for the contrasting impacts of government investment on income inequality, suggested by the underlying theoretical models. These findings are supported, albeit somewhat more weakly by the regressions employing the quintile data. Our general conclusion is that government investment has a mixed effect on income inequality, a conclusion consistent with previous studies.

Appendices

Appendix 1

Appendix 1 provides some of the details supporting the results reported in the text.

1.1 Properties of aggregate transitional matrix

The local transitional dynamics of the aggregate economy summarized by Eq. 7a, b is of the form:

$$ \left( {\begin{array}{*{20}c} {\dot{K}} \\ {\dot{L}} \\ \end{array} } \right) = \left( {\begin{array}{*{20}c} {a_{{11}} } & {a_{{12}} } \\ {\Omega (\kappa a_{{11}} + b_{1} )} & {\Omega (\kappa a_{{21}} + b_{2} )} \\ \end{array} } \right)\left( {\begin{array}{*{20}c} {K - \tilde{K}} \\ {L - \tilde{L}} \\ \end{array} } \right) $$

(A.1)

where $\begin{gathered} a_{{11}} = (1 - g)\left[ {F_{K} + F_{G} G_{K} } \right] - \frac{{(1 - g)}}{\eta }\left[ {F_{{LK}} + F_{{LG}} G_{K} } \right](1 - L) - \delta ;\,\, \hfill \\ \,a_{{12}} = (1 - g)\left[ {F_{L} + F_{G} G_{L} } \right] - \frac{{(1 - g)}}{\eta }\left[ {(F_{{LL}} + F_{{LG}} G_{L} )(1 - L) - F_{L} } \right] \hfill \\ b_{1} = - (1 - g)[F_{{KK}} + F_{{KG}} G_{K} ] > 0;\,\,\,\,b_{2} = - (1 - g)[F_{{KL}} + F_{{KG}} G_{L} ] < 0 \hfill \\ F(K,L,G) = AK^{\alpha } L^{{1 - \alpha }} G^{\nu } ;\,\,\,\,G = \left( {gAK^{\alpha } L^{{1 - \alpha }} } \right)^{{\frac{1}{{1 - \nu }}}} \hfill \\ \Omega = L\left\{ {(1 - \gamma )\left[ {\frac{1}{{1 - L}} - \frac{{(1 - \alpha )}}{{1 - \nu }}} \right] - \frac{{\gamma \eta L}}{{1 - L}}} \right\}^{{ - 1}} ;~\,~\kappa = \left( {1 - \gamma } \right)\frac{\alpha }{K} > 0;\,\,\,\, \hfill \\ \end{gathered}$.

Using the fact that the underlying production function is Cobb–Douglas, together with the steady-state relationships (9a)–(9c), these expressions may be simplified as follows:

$$ a_{{11}} \, = - \frac{{(\alpha - 1)\delta + \nu }}{{1 - \nu }};~~\,a_{{12}} \, = \frac{{(1 - g)(1 - \alpha )}}{{1 - \nu }}\frac{F}{{L^{2} }}\left( {L + \frac{1}{\eta }\left[ {L(1 - \alpha ) + (\alpha - \nu )} \right]} \right) > 0 $$

$$ b_{1} = \frac{(1 - g)\alpha (1 - \alpha - \nu )}{{1 - \nu }}\frac{F}{{K^{2} }} > 0;\,\,\,\,\,b_{2} = - \frac{(1 - g)\alpha (1 - \alpha - \nu )}{{1 - \nu }}\frac{F}{KL} < 0 $$

One can readily show that the determinant of the transitional matrix: $\Omega (a_{11} b_{2} - a_{21} b_{1} ) < 0$, implying that the aggregate transitional dynamic path, summarized by the relationship between $L(t)$ and $K(t)$ is a saddlepoint, the stable path of which is described by

$$ L(t) - \tilde{L} = \left( {\frac{{\mu - a_{11} }}{{a_{12} }}} \right)(K(t) - \tilde{K}) $$

(A.2)

With $a_{12} > 0$, the slope of the relationship (A.2) depends upon ${\text{sgn}} (\mu - a_{11} )$. To determine this we first solve for the stable eigenvalue, $\mu < 0$, in terms of its trace, T, and its determinant, $\Delta$, to obtain $\mu = \left( {{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \right)\left( {T - \sqrt {T^{2} - 4\Delta } } \right)$. Using this expression it is straightforward to show that $\mu - a_{11} < 0$ if and only if $(\kappa a_{11} + b_{1} ) > 0$. Using the above to evaluate this expression, we see that

$$ (\kappa a_{11} + b_{1} ) > 0 {\text{if and only if}} \varepsilon > \frac{[(1 - \alpha )\delta - \nu ]\alpha }{{[1 - \alpha - \nu ](\rho + \delta )}} $$

(A.3)

where $\varepsilon \equiv (1 - \gamma )^{ - 1}$ is the intertemporal elasticity of substitution. Clearly (A.3) is an extremely mild restriction and will hold for any plausible set of parameters.

1.2 Derivation of Eqs. (10) and (11)

Following the procedure outlined in Sect. 3.2.1 yields the following equation in $\dot{k}_{i} (t)$:

$$ \dot{k}_{i} (t) = \frac{{(1 - g)F_{L} }}{K}\left[ {1 - l_{i} (t)\left( {1 + \frac{1}{\eta }} \right) - \left( {1 - l(t)\left( {1 + \frac{1}{\eta }} \right)k_{i} (t)} \right)} \right] $$

(A.4)

To obtain the bounded solution we linearize (A.4) around the steady state. In doing so we note that (9b) and the homogeneity of the production function, imply

$$ (1 - g)[F_{K} \tilde{K} + F_{L} \tilde{L}] - \delta \tilde{K} = \frac{(1 - g)}{\eta }F_{L} (1 - \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{L} ) $$

Using the equilibrium optimality conditions (9c) and labor market clearance then yields

$$ (1 - g)\frac{{F_{L} }}{{\tilde{K}}}\left[ {\tilde{L} - \frac{1}{\eta }(1 - \tilde{L})} \right] = [\delta - (1 - g)F_{K} ] = - \rho < 0 $$

(A.5)

from which we immediately infer the restrictions

$$ \tilde{L} < \frac{1}{{1 + \eta }}~\;{\text{or equivalently}}~\;\tilde{l} > \frac{\eta }{{1 + \eta }} $$

(A.6)

Using (A.6), the bounded solution to (A.4) is

$$ k_{i} (t) - 1 = \omega (t)(\tilde{k}_{i} - 1) $$

where $\omega (t) \equiv 1 + \left( {\frac{{(1 - g)F_{L} (\tilde{K},\tilde{L},G)}}{{\tilde{K}}}\left[ {\frac{{L(t) - \tilde{L}}}{{1 - \tilde{L}}}} \right]} \right)\left( {\frac{{(1 - g)F_{L} (\tilde{K},\tilde{L},G)}}{{\tilde{K}}}\frac{1}{\eta }\left[ {1 - (1 + \eta )\tilde{L}} \right] - \mu } \right)^{ - 1}$.

Substituting (A.5) this expression simplifies to

$$ \omega (t) \equiv 1 + \left( {\frac{{(1 - g)F_{L} (\tilde{K},\tilde{L},G)}}{{\tilde{K}}}\left[ {\frac{{L(t) - \tilde{L}}}{{1 - \tilde{L}}}} \right]} \right)\left( {\rho - \mu } \right)^{ - 1} $$

Using (2a) and (2b) in conjunction with the steady-state conditions we obtain:

$$ \frac{{F_{L} (\tilde{K},\tilde{L},G)}}{{\tilde{K}}} = (1 - \alpha )\frac{{\tilde{F}}}{{\tilde{K}\tilde{L}}} = \frac{(1 - \alpha )(\rho + \delta )}{{\alpha \tilde{L}}} $$

And recalling (9c) we derive:

$$ \omega (t) \equiv 1 + \frac{(1 - \alpha )(\rho + \delta )}{{\alpha \tilde{L}(\rho - \mu )}}\left[ {\frac{{L(t) - \tilde{L}}}{{1 - \tilde{L}}}} \right]. $$

(A.7)

Appendix 2

2.1 List of countries

• (1) Developed OECD countries: Australia, Austria, Belgium, Canada, Czech Republic, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Republic of Korea, Netherlands, Norway, Portugal, Spain, Sweden, United Kingdom, United States.

• (2) Other high income countries: Croatia, Cyprus, Estonia, Israel, Lithuania, Malta, Poland, Slovak Republic, Slovenia, Switzerland.

• (3) Middle income countries Argentina, Belarus, Belize, Botswana, Brazil, China, Colombia, Costa Rica, Dominican Republic, Ecuador, Iran, Kazakhstan, Macedonia FYR, Malaysia, Mexico, Namibia, Paraguay, Peru, Romania, Russian Federation, South Africa, Thailand, Turkey, Uruguay, Venezuela.

• (4) Middle-Low income countries: Bangladesh, Cape Verde, Djibouti, Egypt, El Salvador, Ethiopia, Guatemala, Honduras, India, Indonesia, Lesotho, Mongolia, Morocco, Nigeria, Pakistan, Sri Lanka, Tajikistan, Ukraine.

• (5) Low income countries: Central African Republic, Comoros, Congo, Nepal, Senegal, Tanzania, Uganda.

2.2 List of countries WIID

• (1) High income developed OECD countries: Austria, Belgium, Cyprus, Czech Republic, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Malta, Netherlands, New Zealand, Norway, Portugal, Spain, Sweden, Switzerland, United Kingdom.

• (2) Other high income countries: Croatia, Estonia, Lithuania, Poland, Slovak Republic, Slovenia.

• (3) Middle income countries: Argentina, Belize, Brazil, Colombia, Costa Rica, Dominican Republic, Ecuador, Macedonia FYR, Mexico, Paraguay, Peru, Turkey, Uruguay, Venezuela.

• (4) Middle-Low income countries: El Salvador, Guatemala, Honduras.