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A Mathematical Appendix
We thank Larry Ball, Olivier Blanchard, Suman Basu, Marcos Chamon, Giovanni Dell’Ariccia, Rex Ghosh, Pierre-Olivier Gourinchas, Sebnem Kalemli-Ozcan, Luc Laeven, Alberto Martin, Enrique Mendoza, Jonathan Ostry, Richard Portes, Joseph Stiglitz for helpful comments and suggestions. We also received helpful comments from Itai Agur, Chikako Baba, Varapat Chensavasdijai, Annamaria Kokenyne, Mary Goodman, and Helene Poirson Ward. Korinek acknowledges financial support from the IMF Research Fellowship and from CIGI/INET.
See e.g. Ostry et al. (2011) for an overview of the use of capital controls and Galati and Moessner (2013) for a survey on macroprudential regulation. See also Ostry et al. (2014) for a detailed analysis of the policy considerations involved in choosing between capital controls and macroprudential regulation.
More recently, the IMF (2012) has adopted the term capital flow management measures (CFMs) for capital controls, since the latter term has traditionally had a negative connotation. In this paper, we use the term capital controls in accordance with the tradition in the academic literature.
In some instances, it is difficult to distinguish between capital controls and macroprudential regulation because regulators face a limited set of policy instruments and use one instrument as a substitute for the other. In the current paper, we assume that regulators have both an effective macroprudential instrument and effective capital controls at their disposal. For a more detailed analysis of targeting problems under incomplete instruments see e.g. Ostry et al. (2014).
For a survey of this literature on capital controls see Korinek (2011a). For a survey on macroprudential regulation see Galati and Moessner (2013). A detailed analytic description of the resulting case for capital controls is provided in Korinek (2007, 2010) and Bianchi (2011) in a small open economy with a representative agent. Benigno et al. (2010, 2012, 2013a, 2013b) analyze how the same inefficiencies can be addressed using alternative policy measures. Lorenzoni (2008), Jeanne and Korinek (2010ab), Bianchi and Mendoza (2010) and Korinek (2011b) make the case for macroprudential regulation based on asset price movements that trigger feedback loops. Jeanne (2014) analyzes macroprudential regulation in a framework in which capital controls are by construction a second-best device.
An alternative strand of literature motivates macroprudential regulation and capital controls based on aggregate demand externalities in the presence of nominal frictions. See for example Farhi and Werning (2012, 2013, 2014), Schmitt-Grohe and Uribe (2012), Korinek and Simsek (2014) and Acharya and Bengui (2015).
The East Asian crisis countries include Indonesia, Malaysia, Philippines, South Korea and Thailand.
A country’s real exchange rate is commonly defined as the price of a basket of domestic consumption goods in terms of a basket of international consumption goods. In accordance with our small open economy assumption, we take the price of international consumption goods and traded domestic consumption goods as exogenous. Therefore the price of a domestic consumption basket is a strictly increasing function of the relative price of domestic non-traded goods.
We could refine this constraint by assuming different degrees of pledgeability for traded and non-traded goods but this is not essential to our analysis. We could also impose an equivalent constraint on period 0 borrowing
The assumption that policymakers cannot directly set exchange rates can be relaxed as long as there is a cost associated with doing so. See, for example, Benigno et al. (2013) for exchange rate intervention. Our basic results continue to hold in these cases. Our assumption is also supported by the experience of many emerging economies that were either forced to abandon nominal pegs or experienced strong real depreciations under fixed nominal exchange rates during crises.
As shown by Korinek (2010) and Korinek and Mendoza (2014) and as illustrated by the optimal tax formulas (20), what matters for the magnitude of optimal policy interventions in this class of models is the tightness of borrowing constraints and the response of the borrowing capacity to greater net worth. This is true both in infinite horizon versions and in three period versions of the model like ours. Our calibration is therefore a useful guide for policymakers in countries that find themselves at risk for comparable financial instability to the East Asian crisis countries prior to the 1997 crisis.
In the model setup described above, this is equivalent to setting
If the increase in wealth heterogeneity is accompanied by a simultaneous increase in borrowing capacity in the low state to ϕ(L) = 0.9 in order to match the current account and real depreciation from the 1997 crisis, the optimal capital controls and macroprudential taxes would increase only to 3.1 percent. The intuition is that borrowers are less constrained, the crisis is less severe, and so the required policy intervention is less.