This paper investigates the effects of productive government spending on the relationship between growth and inequality in an economy subject to idiosyncratic production shocks and heterogeneous endowments. Assuming lognormal distributions, we derive tractable closed form solutions describing the equilibrium dynamics. We show how the effect of government investment on the equilibrium dynamics of both inequality and growth depends crucially upon the elasticity of substitution between public and private capital in production. This has important consequences for the growth-and welfaremaximizing rates of government investment. Finally, we supplement our theoretical analysis with numerical simulations, calibrated to approximate the productive characteristics of a real world economy. With the empirical evidence strongly supporting the complementarity between public and private capital, our simulations suggest that conclusions based on the commonly employed Cobb-Douglas production function may be seriously misleading.Key words: Government investment; Idiosyncratic shocks; Growth; Inequality JEL Classification: D31, O41 Revised versionJune 2015*The paper has benefited from comments received on earlier versions from seminar participants at the University of Durham and the University of Pretoria. We also thank Santanu Chatterjee for useful suggestions. Research for this paper was carried out while Getachew was visiting the University of Washington in the Fall of 2013. Turnovsky"s research was supported in part by the Van Voorhis endowment at the University of Washington.**Corresponding author: sturn@u.washington.edu 1 IntroductionThe role of public investment in infrastructure as a source of economic growth continues to be widely debated in both developing and advanced economies, with different economies adopting different policy options. Several emerging-market countries including India, China, and Brazil have undertaken extensive public investment, to which their high growth rates of recent years may at least in part be attributed. In contrast, several European countries have reduced public spending, as they have pursued austerity measures intended to deal with concerns related to their rising debt levels.Contemporaneously with these diverse policies toward public investment, we have witnessed increasing income inequality, both in emerging markets and in most OECD countries. This raises the important question that we address in this paper, namely the relationship between public investment directed toward growth enhancement and its consequences for income inequality.Interest in the relationship between public investment, output, and growth has a long history, dating back to Arrow and Kurz (1970), who examined it in the context of a neoclassical economy.Beginning with Barro (1990), an extensive literature has evolved addressing the issue in an endogenous growth framework, with a general consensus that government spending on infrastructure can yield significant productivity gains and thus enhance growth. See e.g. F...

How much does public capital matter for economic growth? How large should it be? This paper attempts to answer these questions, taking the case of SSA countries. It develops and estimates a model that posits a nonlinear relationship between public investment and growth, to determine the growth-maximizing public investment GDP share. It empirically also accounts for the crowding-in and crowding-out e¤ects between public and private investment, with equations estimated separately and simultaneously, using System GMM. The paper further runs simulation and examines the public investment GDP share that maximizes consumption. This is estimated to be between 8:4 percent and 11:0 percent. The results from estimating the growth model are in the middle of this range, which is larger than the observed value of 7:2 percent at the end of the sample period. These outcomes suggest that, on average, there has been public under-investment in Africa, contrary to previous …ndings. JEL Classi…cation: O4; H4

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How much does public capital matter for economic growth? How large should it be? This paper attempts to answer these questions, taking the case of SSA countries. It develops and estimates a model that posits a nonlinear relationship between public investment and growth, to determine the growth-maximizing public investment GDP share. It empirically also accounts for the crowding-in and crowding-out e¤ects between public and private investment, with equations estimated separately and simultaneously, using System GMM. The paper further runs simulation and examines the public investment GDP share that maximizes consumption. This is estimated to be between 8:4 percent and 11:0 percent. The results from estimating the growth model are in the middle of this range, which is larger than the observed value of 7:2 percent at the end of the sample period. These outcomes suggest that, on average, there has been public under-investment in Africa, contrary to previous …ndings. JEL Classi…cation: O4; H4