Sudden Stops, Productivity and the Optimal Level of International Reserves for Small Open Economies

This paper contributes to the theory of optimal international reserves by extending the Jeanne and Rancière (2011) endowments mall open economy (SOE) model to a SOE with capital and production that explicitly accounts for the main sources of economic growth. A first version of our set-up considers capital as the sole factor of production in the spirit of the AK model of endogenous growth with constant population, implying increasing returns to scale and justified on the grounds of its ability to generate sustained long-run growth, as observed empirically. Under a plausible calibration for typical emerging market countries facing the risk of sudden stops in capital inflows, we find that the optimal ratio of international reserves to output is 1.7%, which is quite lower than that in Jeanne and Rancière (2011), of 9.1%, even if calibrated to the same sample of 34 middle-income countries. A richer version then introduces also labour as a second factor in a conventional labour- augmenting Cobb-Douglas production function with constant returns to scale and exogenous population growth, consistent with a long-run balanced growth path and the sustained per capita income growth in the data. Under this alternative technology and the same calibration, we find that the optimal reserves-to-output ratio for emerging market SOEs is 5.5%, almost identical to the 6% obtained by Bianchi et al. (2018) in a different, sovereign debt model without capital and production. We conclude that our results are explained by the role of capital accumulation as precautionary saving: the accumulated capital stock can potentially be used as a pledge to external creditors in obtaining borrowing, therefore insuring better a SOE against sudden stops.