Abstract
This paper studies the positive and normative effects of alternative monetary and exchange rate polices in a small open economy model subject to occasional “sudden stops” associated with binding borrowing constraints. Borrowing constraints in the model depend on endogenous movements in asset prices. We find that in normal times, there is little difference between alternative exchange rate policies. But during a crisis, macroeconomic outcomes are far worse under a pegged exchange rate regime. Under some shock configurations, crises may be less frequent under a pegged exchange rate regime, but the worse performance during a crisis leads the pegged exchange regime to be inferior to the floating regimes. Finally, we show that in the presence of pecuniary externalities in asset prices, there may be a case for a fiscal authority to subsidize capital inflows at a constant rate. But the benefits of capital inflow subsidies are much weaker under pegged exchange rates.
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Notes
This form of preference simplifies the computational procedure for the model, but does not play a key role in the qualitative analysis.
Kiyotaki and Moore (1997) type of credit constraint is widely used to study business cycles, recent papers including Iacoviello (2005), Liu and others. (2013, 2016) and others. The specification is based on the notion that the creditors ensure that they receive the real value collateral in terms of foreign goods, in the event of default. An alternative specification uses the current value of assets as collateral (see Mendoza, 2010; Bianchi, 2011 and many other papers). When shocks are quite persistent, as in our framework, the two specifications have similar implications, because a fall in asset prices in that case reduces both the current and expected future value of collateral assets.
The presence of working capital serves as an amplifier when the credit constraint binds. The intra-period loan and inter-period loan are determined jointly, both of which suffer from contract enforcement problem. Imposing that the working capital loan be inter-period rather than intra-period would lead to additional dynamics that would make the model harder to solve, but because it would affect economic activity through the same channels as before, would have little impact on the results of the paper.
Since the interest rate on foreign borrowing is exogenous in any case, this assumption has no effect on the model’s dynamics.
The constraint (6) introduces a number of potentially conflicting factors governing the effects of exchange rate adjustment. In principal, one could expect that it might make exchange rate flexibility less desirable, because unexpected exchange rate depreciation which is persistent would tighten the constraint. While this is true in principle, in the quantitative analysis we find that the deflationary pressures coming during a crisis under an exchange rate peg completely overwhelm any of the compensating effects attached to a reduced expected rate of depreciation on the expected value of collateral.
Note that the change in the nominal exchange rate is a function of the change in the real exchange rates and inflation, \(\mathcal {E}_{t}/\mathcal {E}_{t-1}=\pi _{t} e_{t}/e_{t-1}\). Therefore, stabilizing nominal exchange rates and inflation is equivalent to stabilizing both inflation and the real exchange rate.
A more complete account of this optimal monetary policy in a related context is given in Devereux and others (2015).
Increasing \(\kappa _{H}\) does not change the results since the borrowing constraint almost never binds when \(\kappa _{H}=0.45\).
In the Appendix, we show that absent TFP shocks output volatility is higher in the peg than under the inflation targeting regime.
We note that the model calibration is based on the presence of price rigidities, and outside of the crisis, under the standard calibration, price rigidities are not so severe. Our results for exchange rate regime comparisons in normal times are in general consistent with those in the New Keynesian literature. When there are price and wage rigidities, the differences between inflating target and optimal monetary in normal times are much larger (see Devereux and others 2015). Note also that the result that all three regimes are similar, outside crisis times, also holds separately for different combinations of the three shocks in the model, and does not depend upon the presence of any one shock in particular.
Note that these results imply that the movements in the exchange rate are beneficial for the economy in a crisis. This is not the case by construction. The exchange rate has positive effects on the economy through the expenditure-switching channel. But an exchange rate depreciation may also raise the external debt burden and the degree to which the collateral constraint binds. A depreciation which persists into the next period increases the value of foreign debt repayment in domestic currency and makes it more likely that the constraint binds. In the baseline calibration, we find that the first channel dominates the second one, so that a depreciation is expansionary.
This result would be qualified where we introduce nominal wage stickiness in addition to price stickiness in the model. See Devereux and others (2015).
As the Appendix shows, if the model is driven only by foreign interest rate shocks and leverage shocks, the frequency of crises is almost the same under all exchange rate arrangements. Note that the finding of different crisis probabilities across regimes is a combination of two factors, the degree of precautionary saving and the nature of shocks. Under all different shock combinations, there is a larger degree of precautionary saving under the peg. But the difference is most stark with productivity shocks. With productivity shocks, the impact of a crisis under a peg, relative to the floating exchange rates regimes, is most extreme, so savings is greater under a peg so as to reduce the probability of a crisis. But also the nature of the response to the productivity shock is different across the regimes, as discussed above. In the absence of productivity shocks, both factors are present also, but because the impact of a crisis is less pronounced across regimes in that case, the probabilities of a crisis are similar in all cases.
This is not exactly true. As to be expected, the optimal monetary policy regime will raise conditional welfare through the more accommodative policy during a crisis. But the effect is negligible up the to accuracy calculated by our solution.
Schmitt-Grohe and Uribe (2013) establish a similar result in the case of downward wage rigidity.
This policy will in general be time inconsistent, in the absence of a commitment technology. As shown in Devereux and others (2015), the time-consistent policy is to impose a capital tax during a crisis, and in equilibrium, this will lead to lower welfare than in the absence of a tax.
In evaluating the benefits of capital subsidies, it is important to use a conditional welfare measure. As described in the Appendix, conditional welfare incorporates the transitional benefits to domestic households from being able to front load consumption, given that their rate of time preference exceeds the world interest rate. The impact of the policy on the unconditional welfare measure is likely to be quite different. Since a capital subsidy shifts out the stationary distribution of debt in the economy, in general a subsidy will tend to reduce unconditional welfare, as we show below.
We do not solve for the optimal subsidy, which in general will be time varying and depend on the degree to which the collateral constraint binds. The full solution of the optimal capital tax/subsidy profile with commitment turns out to be a particularly difficult computational problem in this model, since it involves keeping account of past state variables which represent “promises” of the fiscal authorities made in the past. Nevertheless, as discussed above, it is shown in Devereux and others (2015), Appendix D, that, in general, an optimal policy with commitment will subsidize capital inflows during a crisis, when the collateral constraint binds.
Conditional welfare reaches a maximum as we increase the subsidy rate under the floating exchange rate regime, but our solution method becomes less accurate, since we need to expand the domain progressively as the subsidy is increased. While the implied optimal subsidy under flexible exchange rates may be unrealistically large, if we were to add the realistic feature that subsidies had to be financed with distortionary taxation, the optimal subsidy would be in a much more modest range.
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*Michael B. Devereux is with the Vancouver School of Economics at University of British Columbia and NBER and CEPR; and his email address is: devm@mail.ubc.ca. Changhua Yu is with the China Center for Economic Research, National School of Development at Peking University and his email address is: changhuay@gmail.com. We are grateful to the helpful discussion by Tommaso Monacelli and comments from Maury Obstfeld, Pau Rabanal, Raphael Schoenle, and participants at the conference “Exchange Rates and External Adjustment” organized by Swiss National Bank, International Monetary Fund, and IMF Economic Review, Zurich, June 24–25, 2016. We also thank the editor, Pierre Olivier Gourinchas and two referees for detailed comments on the paper. Devereux thanks the Social Science and Humanities Research Council of Canada for financial support. Yu thanks the National Natural Science Foundation of China 71303044.
Appendices
Appendix A Model Moments without Productivity Shocks
See Figure 7 and Tables 5, 6, 7.
This Figure Compares Second Moments for the Key Variables in the Model for Different Combinations of the Three Shocks in the Model, Where the Comparison is Across the Three Regimes of Strict Inflation Targeting, Ramsey Optimal Monetary Policy, and the Exchange Rate Peg
Appendix B Measures of Welfare
The lifetime utility for a representative household in the small economy conditional on the initial debt level and exogenous shocks can be written as
We define a certainty equivalence of effective consumption \(\widetilde{C(b^{*}_{0},Z_{0})}\) in a policy regime conditional on an initial state (\(b^{*}_{0},Z_{0}\)) as
Rearranging the equation yields
We will use \(\widetilde{C(b^{*}_{0},Z_{0})}\) to measure conditional welfare in the main text.
The unconditional welfare is measured in a similar way except that the welfare Wel is a weighted average of conditional welfare \(Wel(b^{*}_{t},z_{t})\) over the whole domain in the stationary equilibrium.
