Monetary policy in a dual currency environment

Abstract

We develop a small open economy general equilibrium model with sticky prices and partial dollarization – a situation where both domestic and foreign currencies coexist. We derive a tractable representation of the model in terms of domestic inflation and the output gap in which a trade-off, which depends on the degree of dollarization, arises endogenously due to the presence of foreign interest rate shocks. We use this framework to show analytically how higher degrees of dollarization induce larger volatilities of the output gap and inflation, thus hampering a central bank’s effectiveness to stabilize the economy. Our impulse response functions show that the transmission of such shocks has a positive (negative) effect on inflation and negative (positive) effect on the output gap when money aggregates and consumption are complements (substitutes).

Keywords:

• dollarization
• currency substitution
• policy trade-off
• staggered price setting
• open economy

JEL Classification:

• E50
• E52
• F00
• F30
• F41

Acknowledgement

We would like to thank Nicoletta Batini, Jess Benhabib, Pierpaolo Benigno, Paul Castillo, Luca Colantoni, Roberto Chang, Thomas Cooley, Mark Gertler, Ricardo Lagos, Gonzalo Llosa, Paul Levine, Carlos Montoro, Sydney Ludvigson, Fabrizio Perri, and seminar participants at the Central Bank of Peru and the 2002 meeting of LACEA for helpful comments.

Notes

1. See Armas et al. (2007) for a description of the main channels through which partial dollarization hampers the transmission mechanism of monetary policy.

2. This percentage approximates the share of transactions in dollars relative to total transactions by combining data on (i) ATM dollar withdrawals; (ii) dollar checks; (iii) dollar interbank transfers and (iv) direct debits in dollars.

3. Castillo et al. (2012) estimated a dynamic stochastic general equilibrium (DSGE) model with partial dollarization using Bayesian techniques and the Peruvian data.

4. Partial dollarization can also be motivated using shopping time models. Castillo (2006) model currency substitution by adding transaction frictions in a cash-in-advance model.

5. Clarida et al. (2001, 2002) assumed the presence of an exogenous cost-push shock in order to generate the trade-off between inflation and output gap.

6. There is now lengthy literature for small open economies that show that dollarization of liabilities affect the aggregate demand through balance sheets effect (debt denominated in either domestic or foreign currency). Some prominent examples include Gertler et al. (2007), Christiano et al. (2003) and Céspedes et al. (2004). In contrast with these studies, our set-up will affect both aggregate demand and aggregate supply by the effect of currency substitution over the MUC.

7. As shown in Castillo et al. (2012) this formulation is supported by the Peruvian data.

8. Note that consumption and money aggregates are complements. For the particular case when σ = 1, the condition simplifies to . Then if 0 > ω < 1 C and Z are complements, on the contrary if ω > 1 consumption and the overall aggregate are substitutes U_CZ < 0.

9. See Woodford (2003, chapter 2) for a brief discussion related to the consequences of nonseparable utility function and price determination.

10. Notice that money shows up in both the budget constraint and in the utility function. In our model, the monetary distortion is taken to be nongnegligible or nontrivial. Moreover, nonseparability between money aggregates and consumption, guarantee a role for money even if monetary policy actions are defined in terms of an interest rate feedback rule.

11. Note that when b = 1, the model is similar to the small open economy version presented by Clarida et al. (2001).

12. Even with low inflation levels, agents still demand foreign currency not only as an mean of exchange but also as deposit of value.

13. Obstfeld and Rogoff (1996) assumed a quadratic form as they consider an economy with legal restrictions in holding foreign currency. The form they consider is , where the second term measures the evasion costs of the legal restrictions.

14. A model with transaction technology with shopping time and real money balances in both foreign and domestic currencies would be another possibility at the cost of losing tractability. See Brock (1974) for an earlier use of shopping-time model to motivate a money-in-the-utility function approach. The advantage of the way we impose currency substitution is that it delivers a more tractable model. Other approaches to give rise to a valued role for money are suggested by Kiyotaki and Wright (1993) by imposing that direct exchange of commodities is assumed to be costly, but there is a fiat money that can be treated as costlessly for commodities.

15. Unlike Gali and Monacelli (2005) and Clarida et al. (2002), we rely on a complete general equilibrium structure. As you will see later, in steady state, γ will represent the share of domestic consumption allocated to imported goods, so it could be interpreted as a natural index of openness. So in this sense, (1 – γ) is interpreted as the degree of home bias and the larger this value (smaller γ) the closer to a closed economy counterpart.

16. Given this assumption, it is not necessary to characterize the current account dynamics in order to determine the equilibrium allocations.

17. Given that markets are complete internationally, it does not matter the currency denomination of the securities.

18. Therefore, is a price of one unit of nominal consumption of time t + 1, expressed in units of nominal consumption at t, contingent on the state at t + 1 being s_{t + 1} and given any state s in t. If we define the value of the portfolio at the end of the period as A_t, the complete market assumption implies that there exists a unique discount factor of a portfolio with the property that the price in period t of the portfolio with random value B_{t + 1} is .

19. The interest rate at home is the price of the portfolio that delivers one unit of home currency in each contingency that occurs one period ahead.

20. We assume complete markets for simplicity and tractability. For small open economy models with incomplete markets and stationary net foreign assets see Schmitt-Grohe and Uribe (2003) and Laxton and Pesenti (2003).

21. Relaxing this assumption would give interesting results, however, since the main goal of the article is to derive a model for a partially dollarized economy, the assumption of completeness is reasonable to get a tractable model.

22. The UIP holds even if we have deviations from purchasing power parity PPP. In an incomplete markets structure without financial frictions (also known as the ‘bond economy’), the UIP will also hold in log-linear form. However, we can attain deviations from the UIP once financial frictions are taken into account.

23. The derivative can be positive or negative depending on the size of . If , then . If , then .

24. is the stochastic discount factor associated with the first-order condition for the recursive competitive equilibrium.

25. In an appendix available upon request from the authors, we provide details on the derivation.

26. Laxton and Pesenti (2003) find that inflation-forecast-based rules may perform better in small open economies than conventional Taylor rules.

27. In the Peruvian economy, since the adoption of a full-fledge IT regime in 2002, the monetary policy has been conducting by targeting the inter-banking interest rate. Before that period, the central bank was implementing its monetary policy by targeting money aggregates. It has been observed a significant reduction of the mean in nominal variables in the more recent period as a consequence of the change in the instrument.

28. corresponds to an interest rate peg in the flexible price allocation, not a zero nominal interest rate.

29. Details of the derivation are available in an appendix upon request from the authors.