Optimal public investment with and without government commitment
Pierre-Daniel G. Sarte
We analyze the problem of optimal public investment when government purchases of productive capital assets are financed through income taxes. Virtually all previous work in this literature has prescribed a share of public investment in GDP that is both constant and time consistent. This paper shows that this straightforward prescription derives from specific assumptions relating to preferences and technology. In a more general framework, the optimal policy is neither constant nor time consistent. With full commitment, a policymaker will typically choose a tax rate, or alternatively a share of public investment, that increases over time. He does not exploit the first-period non-distortionary tax on capital but instead delays taxation in order to generate a "take-off" phase with higher consumption and higher private investment. When optimal policy is constrained to be time consistent, long-run tax rates surprisingly emerge to be lower than under the Ramsey plan. Therefore, the inability to commit to future policy implies too little public investment in the long run. Finally, in contrast to previous work, we find that the efficient share of public investment in GDP depends importantly on the intertemporal elasticity of substitution, capital depreciation rates, and the growth rates of productivity and population.
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