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CEPR, University of British Columbia, and International Monetary Fund. CEPR and University of St Andrews. We thank Philippe Bacchetta, seminar participants in Georgetown University, the Board of Governors of the Federal Reserve System, and Johns Hopkins University for comments. This research is supported by the ESRC World Economy and Finance Programme, award number 156-25-0027. Devereux also thanks SSHRC, the Bank of Canada, and the Royal Bank of Canada for financial support.
Nevertheless, both papers conclude that, for reasonable quantitative estimates over parameters and volatilities, price stability represents a close approximation to an optimal policy. See also Devereux (2004).
The method of Devereux and Sutherland (2006a) is fully general, however, and is not restricted to models simple enough to be characterized analytically.
Firms earn monopoly profits because each firm is the monopoly supplier of a differentiated good. Note also that, because the home agent receives all home profits, in a symmetric equilibrium with zero net foreign assets (Wt = 0), gross portfolio holdings exactly offset each other in value terms. This is simply an accounting convention which simplifies the development of the model, but it is not at all critical. It is easy to treat all profit income as traded on a stock market (so that wage earnings represent the home residents’ only non-portfolio income). In this case, even in a symmetric equilibrium with zero net foreign assets, agents in each economy would have non-zero net portfolio positions. The solution method for optimal portfolios applies equally to this environment.
In an incomplete markets environment, there is an open question as to what determines the discount factor Ωt+i. If firms are to discount future profits at the same discount rate as their shareholders, then both home and foreign intertemporal rates of substitution would need to enter into the firm’s evaluation of future profits. Fortunately, at the level of approximation in which the portfolio solution is obtained, any time variation in the firm’s discount factors drops out. Since all the non-portfolio equations in the model are evaluated by linear approximation around a steady state without growth, the discount factor at this level of approximation will simply be β, the common subjective time discount factor of consumers. As a result, the price dynamics of the model are identical to those of the standard producer currency pricing model of Benigno and Benigno (2005), for instance.
We think of this as a financial market shock.
In effect, our solution for
For the purposes of taking approximations, we assume that the innovations are symmetrically distributed in the interval [−ε, ε]. This ensures that any residual in an equation approximated up to order n can be captured by a term denoted O (εn +1)
The notation for returns is slightly different. We define
The wealth dynamics of the model have a unit root for the same reason as in many open economy models. It would be possible to eliminate the unit root by assuming endogenous time preference or imposing a portfolio adjustment penalty (see for instance, Schmitt Grohe and Uribe 2004). But this would have minimal consequences for our results. What matters for the equilibrium portfolio is the conditional one-step ahead moments of consumption and returns. These conditional statistics are always well defined in our model. Imposing an added structure on the model to eliminate the unit root would not affect the method of construction) of
Devereux and Sutherland, (2006a) provide a complete development of this solution method and discuss more fully the reasons why time variation in portfolios plays no part in the solution process. If it is desired to analyse time-variation in portfolios, it is necessary to approximate the portfolio selection equation up to a 3rd order, and the rest of the model’s equilibrium conditions up to a 2nd order. This would capture the way in which conditional moments evolve over time depending on persistent movements in the state variables of the economy. For a complete analysis, see Devereux and Sutherland (2006b). See also Tille and Van Wincoop (2007).
To simplify the notation, we also assume that
This result does depend on the configuration of shocks, the structure of the model, and the monetary policy specification. Under a monetary targeting rule for monetary policy, an optimal bond portfolio may involve a long (short) position in foreign currency (home currency) bonds, even when θ > 1.
In this case the negative welfare impact of a terms-of-trade decline following an increase in u is greater that the positive welfare effect of higher home GDP.
This is because both relative consumption (as in (DC)) and relative equity returns respond to productivity shocks in proportion to (1−θ).
Home bias is equivalent to a value of
As noted above, all conditional variances are well defined, even though there is a unit root in the wealth distribution.
If productivity disturbances were temporary, then non-contingent bond trade would offer some risk sharing benefits. In this case also, monetary policy can enhance the sharing of consumption risk due to productivity shocks, but it still cannot achieve fully efficient risk sharing.
We do not explore in detail the nature of these alternative rules. See Benigno (2001) for an elaboration, within a model almost identical to our NC economy.
It is important to see that this result does not depend on our restricted class of monetary rules. Any monetary policy rule that generates full risk sharing can be fully optimal only if it also supports price stability. Even in the case λ = 0, an optimal monetary policy using a wider class of monetary rule than (monrule) will ensure that the nominal exchange rate responds efficiently to productivity shocks, and domestic PPI inflation is zero.
For λ = 0, the volatility of the trade balance is always higher in the NBE economy. But for a high degree of price stickiness, this conclusion may be reversed.