| Summary: | Making three distinct contributions to the literature on international reserves for small open economies (SOEs), this thesis is composed of three main chapters. Chapters 1 and 2 contribute to the underlying theory of optimal international reserves, extending the Jeanne and Rancière (2011) endowment SOE model to a production economy, each using one of the most common technology specifications in Neoclassical growth theory. Chapter 3, then, examines empirically key aspects of reserve holdings as observed in a dataset of high and low middle income emerging market economies (EMEs) used in the calibration of the preceding theoretical chapters. Chapter 1 explores the effects of investment and production on optimal reserves in SOE EMEs and derives an optimal reserves-to-output formula in the case where capital is the sole factor of production as in the AK model of endogenous growth. We refer to this version as the one-factor production SOE AK model, or simply the AK model (of endogenous growth). This version implies increasing returns to scale (IRS) and is justified on the grounds of the ability of the AK model to generate endogenously, via the influence of policy – such as subsidies or taxes on investment – on capital accummulation, sustained long-run growth observed in the data. We find that the endogenous growth AK model with IRS implies a negative relationship between the optimal reserve-to-output ratio and capital-augmenting (in fact, here sole-factor) technological progress. Depending on the calibration of the productivity parameter, the model quantifies the optimal ratio of reserves to output at 1.74% for SOEs. Chapter 2 introduces labour, making the production function more general. More precisely, we switch to a conventional labour-augmenting Cobb-Douglas (CD) production function, which embodies alternative assumptions of constant returns to scale (CRS) overall – but with diminishing returns to scale (DRS) for each of the two factors, capital and labour – and convergence to a balanced growth path (BGP) in the long run. In turn, this version is justified on the grounds of being consistent with a long-run BGP in Neoclassical models of exogenous growth and with sustained per capita income growth in these models. The second chapter thus focuses on the effects of labour-augmenting productivity on the optimal reserves-to-output ratio in a production SOE. Moreover, the alternative modelling of the production function, IRS AK versus CRS CD, and the type of growth, endogenous versus exogenous, allows us to compare the analytical results in chapter 1 (AK model) with those in chapter 2 (the CD model). Similarly to the endogenous growth AK model, we find that in the exogenous growth CD model along the BGP labour-augmenting technological progress decreases the optimal reserves-to-output ratio. Depending on the calibration of the labour-augmenting productivity parameter, the CRS CD model quantifies the optimal ratio of reserves to output at 5.5% in the richer two-factor production SOE model. This roughly three times higher ratio of optimal reserve holdings to output arises from the difference in the specification of technology in the production functions. This ratio is still quite lower than the corresponding one derived in the endowment SOE model of Jeanne and Rancière (2011), 9.1%. The main reason for optimally maintaining a lower ratio of international reserves to output in a production SOE with investment and productive capital relative to the endowment SOE benchmark is as follows. With the capital stock now accumulated via investment and potentially used as a pledge to external creditors in obtaining borrowing and therefore insuring better against sudden stops, the optimal reserve-to-output ratio is much lower relative to an otherwise similar endowment economy in the AK model. As depreciation depletes the existing capital stock, opposite to investment, the reversal of the relationship is not surprising in both the AK and CD models. Whereas the AK model can generate endogenously, via policy, persistent capital accummulation leading to sustained long-run growth, adding labour as a second factor in a CD production function, consistent with a long-run BGP in Neoclassical models of exogenous growth and with sustained per capita income growth, results in a roughly mid-point optimal reserve-to-output ratio of 5.5%. Chapter 3, finally, takes a complementary, statistical approach and examines the key theoretically derived determinants of international reserves relative to output together with the most common empirically motivated determinants suggested in the literature as ‘control variables’ in a dataset of 26 high and low middle income economies. For this purpose, we initially estimate a pooled OLS benchmark and a panel data fixed effect model to analyse the relative importance of such empirically measured determinants of real-world reserve holdings as well as possible country specificities. We then use quantile regression techniques to examine the variation in these determinants across the reserve holdings distribution in our sample. We examine the uniformity of coefficients by several quantile regressions and the overall models. Our quantile regression results suggest that there is substantial variation in middle income countries in terms of the reserve holdings distribution. Our findings from inter-quantile regressions show that there are statistically significant differences in share of imports in GDP, investment share of GDP, and short term external debt to GDP.
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