I. Introduction

The growth in the size and complexity of international financial markets has been one of the most striking aspects of the world economy over the last decade. Lane and Milesi-Ferretti (2001, 2006) document the increase in gross holdings of cross-country bond and equities for a large group of countries. They describe this as a process of financial globalization. Economists and policy makers have speculated on the implications of financial globalization for the design of monetary policy². There are many aspects to this question. Most central banks now either explicitly or implicitly follow a policy of inflation targeting. Under this policy, price stability, appropriately defined, is the principal goal of monetary policy. Is this conclusion altered by the presence of large cross country gross holdings of financial assets, where movements in asset prices and exchange rates may have significant wealth redistribution effects? In addition, should policy-makers be concerned about asset prices directly, rather than focusing on inflation in goods prices?

This paper constructs a two-country open economy model with endogenous portfolio choice. We can address the questions raised above, because our model determines the structure of gross holdings of cross-country financial assets. Our principal finding is that endogenous portfolio structure does not alter the case for price stability as an optimal monetary policy. In fact, it may even reinforce this case. In an environment where financial markets are incomplete, price stability is desirable because it enhances the international risk-sharing properties of nominal assets, even without nominal goods price rigidities.

An intellectual foundation for price stability in monetary policy has been given by King and Wolman (1989), Woodford (2003), and others. They have sticky-price dynamic general equilibrium models where a monetary rule devoted to stabilizing prices eliminates the inefficiency of costly price adjustment. In an open economy, the optimality of price stability as the sole goal of monetary policy depends on the structure of international financial markets. Benigno (2001) and Obstfeld and Rogoff (2002) show that the absence of full international risk-sharing may interact with the inefficiency arising from sticky prices, so that price stability may not constitute the unique optimal goal of monetary policy³.

A drawback of many of these papers is that international financial markets are modeled in a very rudimentary way. Financial markets are typically represented either by the absence of any type of international risk-sharing (e.g. trade in non-contingent bonds) or by full risk-sharing (complete markets). In reality, international financial markets are likely to be somewhere in the middle. In addition, previous literature has not distinguished gross from net cross-country asset holdings. Once we allow for endogenous portfolio choice, it is possible that monetary policy impacts on the structure or efficiency of international financial markets. And as mentioned, the presence of large gross holdings of different financial assets may in turn have repercussions for the choice of optimal monetary policy. Thus, the analysis of monetary policy with endogenous international portfolio structure is an important direction for this literature.

Until recently however, the analysis of portfolio structure in dynamic general equilibrium macro models was impeded by the difficulty in solving the higher order aspects of these models that are required to determine optimal portfolios, while retaining enough tractability to analyze the general equilibrium impact of shocks and monetary policy. This paper resolves this difficulty by making use of some recent results on the approximation of optimal portfolio choice in general equilibrium. We apply a methodology developed in Devereux and Sutherland (2006a), which shows how to incorporate optimal portfolio choice in a standard dynamic general equilibrium macro model in a tractable way. This is combined with an otherwise standard two-country model of an open economy with staggered price-setting, stochastic productivity and interest rate shocks, and monetary policy governed by an interest rate. The model is then solved under a number of financial market configurations, differing in the range of assets that are traded across countries. In the least complex of these, the only financial asset is a non-contingent real bond, and there is essentially no portfolio choice at all. In the most complex, there is trade in nominal bonds and equities, and given our stochastic environment, markets are complete. In an intermediate case, nominal bonds denominated in each country’s currency can be traded. In this intermediate case, portfolio choice is endogenous, but asset markets are incomplete.

The model is simple enough to produce analytical solutions for gross asset holdings under each financial market configuration, and show how these depend on the stance of monetary policy, the relative importance of shocks, and the degree of price stickiness⁴. We can then use these results to ask how monetary policy interacts with portfolio choice in affecting macroeconomic outcomes, to investigate how monetary policy influences the degree of international risk-sharing, and to characterize an optimal monetary. Since the stance of monetary policy determines the stochastic properties of inflation and the nominal exchange rate, it affects the properties of returns on both nominal bonds and equities, which in turn govern both the endogenous portfolio choices of agents as well as the equilibrium degree of international risk-sharing.With trade in both bonds and equities, there are complete markets, and all possible international risk-sharing is exploited, for any monetary policy. Then we find that the portfolio composition of bonds and equities is independent of the monetary policy rule. Thus, under complete markets, there is no interaction between country portfolios and monetary policy. Then price stability is an optimal policy for conventional reasons, since it eliminates the welfare losses coming from slow price adjustment.

On the other hand, when assets markets are restricted to trade only a real non-contingent bond, the results of Benigno (2001) and Obstfeld and Rogoff (2002) apply. A monetary policy that deviates from price stability would in general be desirable, so as to alleviate risk-sharing inefficiencies.

But in the intermediate case, with international trade in nominal bonds, the implications for monetary policy are substantially different. In this case, asset markets are incomplete, and the monetary policy rule does affect the composition of countries portfolios. Monetary policy actually plays a dual role. First, it can be used so as to support the flexible price equilibrium of the economy, as in the standard model. In general, we would expect such a policy not to be fully optimal, due to market incompleteness. But this does not take account of the secondary role of monetary policy. Monetary policy can enhance the degree of international risk-sharing itself, by improving the risk-hedging properties of nominal bonds in optimal portfolios. This second property of policy is conceptually independent of the first. In fact, it remains useful even in a flexible price economy. Our results show that in an environment where nominal bonds are traded, a policy of strict price stability will endogenously generate full international risk-sharing. Strict price stability is therefore desirable on both counts. It supports the flexible price outcome, and it also allows nominal bond returns to offer full risk-sharing against country specific productivity shocks. Moreover, even if prices are fully flexible, with incomplete asset markets there is still a non-trivial welfare case for price stability.

More generally, the results imply that financial globalization does not affect the fundamental aims of monetary policy. Although our model produces a international financial structure where countries are holding large offsetting gross nominal asset positions, so that exchange rate movements can generate substantial ‘valuation effects’, the presence of these effects does not directly change the optimal monetary rule. Because portfolios are chosen optimally, the wealth redistribution arising from exchange-rate-induced valuation effects represent the workings of an efficient international financial structure. Moreover, monetary authorities do not have to be concerned with these redistributions. It is still the case that monetary authorities are best to use the exchange rate in the traditional Friedman (1953) manner - to generate efficient terms-of-trade adjustment. The new insight from this paper is that it may be desirable to have the nominal exchange rate play the same role as in Friedman’s analysis, even without his underlying assumption of sluggish nominal goods price adjustment.

Our results do show however that the effects of monetary policy on other variables may be very different in a model with endogenous portfolio choice than in the standard analysis. Because the monetary rule leads to changes in the structure of international portfolios, the effects of monetary policy may be the opposite of what traditional reasoning would imply. For instance, a policy putting more weight on price stability may increase rather than reduce exchange rate volatility and the volatility of international capital flows. Because the exchange rate represents the excess return on nominal bonds, this means that an optimal monetary policy may increase rather than reduce asset price volatility.

This paper is related to a growing literature on the analysis of portfolio composition and financial markets in dynamic general equilibrium models. As mentioned, the method we use is developed in Devereux and Sutherland (2006a). Related papers are Engel and Matsumoto (2006), Evans and Hnatkovska (2006), and Kollmann (2006). Engel and Matsumoto (2006) incorporate endogenous portfolio choice into a complete markets version of a sticky-price open economy macro model, focusing on the ‘home equity bias’ puzzle. They do not directly analyze the role of monetary policy. Kollmann (2006) and Evans and Hnatkovska (2005) construct non-monetary dynamic general equilibrium environments with endogenous portfolio choice. Kollmann’s (2006) analysis is based on complete markets, also examining the determinants of home equity bias. Evans and Hnatkovska (2005) employ a numerical approximation method to solve for portfolio choice⁵.

A slightly older literature has examined the determinants of trade in nominal bonds. Svensson (1989) develops a stochastic, two country, two period cash in advance model to analyze the determinants of nominal bond trading and the welfare gains to asset trade, but does not characterize the specific gross portfolio positions or the determination of optimal monetary policy. Bacchetta and Van Wincoop (2000) also develop a two period endowment economy model, and obtain optimal portfolios in a model where equity and nominal bonds are traded. They focus on the impact of nominal bonds on capital flows. An early fundamental contribution is Helpman and Razin (1978).

The next section develops the open economy model. Section 3 discusses the approach to solving for optimal portfolios. Section 4 solves for the optimal portfolios and discusses the effects of monetary policy on portfolios. Some conclusions follow.

II. An Open Economy Macro Model

We develop a basic two-country open economy model. There is a ‘home’ and ‘foreign’ country, with each country being specialized in a particular range of products. Households maximize utility over an infinite horizon. It is assumed that consumers in each country can trade in a range of financial assets. We vary the menu of available assets, but at its most extensive there are four assets, consisting of home and foreign equity shares, and home and foreign nominal bonds. The payoffs to each of these assets are defined below. We also allow for two types of shocks; interest rate (or financial market) shocks, and shocks to productivity, in each country.

III. Solving the model

The full solution to the model is described by the sequence {C_t, ${\stackrel{⌢}{P}}_{H,t}$, ${\stackrel{⌢}{P}}_{F,t}$, P_H,t, P_Ft, S_t, Y_t, $Y_t^{*}$, R_t, $R_t^{*}$}, {r_1,t..r_N,t}, and the vector α_t = {α_1,t..α_N,_t } which solves equations (5)-(7), (9)-(11) and the equivalent equations for the foreign economy. It is well known that, except in very special cases, it is not possible to obtain analytical solutions to dynamic general equilibrium models of this type, even without endogenous portfolio choice. This difficulty becomes more extreme when we allow for a menu of independent assets and endogenous portfolio choice, particularly when markets are incomplete.

The open economy macro literature typically analyzes this model by the method of first-order approximation of all the necessary conditions of the model around a non-stochastic steady state. But, up to a first order approximation, the value of α_t is indeterminate, because at this level of approximation all assets are perfect substitutes. The existing literature therefore tends to confine attention to asset market structures where the portfolio allocation problem is not relevant. In this section, we describe our method for obtaining optimal portfolio shares by means of a particular second-order approximation approach. In particular, we show that it is necessary to increase the order of approximation, so as to incorporate terms involving risk, but one only needs to do this for the portfolio selection equation, (7). The rest of the model conditions can be approximated only up to the first order. This solution method makes it possible to analyse the above model with any asset market structure.

B. Linear approximation to the rest of the model

In order to obtain the solution given in (20), we need to construct the linear approximation for the non-portfolio equations in the model. The linear approximation of the home country budget constraint is given by (17). Taking a linear approximation of the Euler equations implies that

$\begin{array}{ccc}{E}_t{\stackrel{⌢}{C}}_{t+1}-{\stackrel{⌢}{C}}_t=E_t{\stackrel{⌢}{r}}_{N,t+1}& & (21)\end{array}$

The equivalent condition for the foreign economy is

$\begin{array}{ccc}{E}_t{\stackrel{⌢}{C}}_{t+1}^{*}-{\stackrel{⌢}{C}}_t^{*}=E_t{\stackrel{⌢}{r}}_{N,t+1}+E_t{\stackrel{⌢}{Q}}_{t+1}-{\stackrel{⌢}{Q}}_t& & (22)\end{array}$

Note that, in these expressions, and all those that follow, we omit the residual term, O (ε ²) Up to a first order approximation, it must be the case that $E_t{\stackrel{⌢}{r}}_{k,t+1}=E_t{\stackrel{⌢}{r}}_{N,t+1}$, for all k = 1..N −1. Therefore, using the policy rule (10) and the definition of the real return on home country nominal bonds, we have:

$\begin{array}{ccc}\gamma ({\stackrel{⌢}{P}}_{H,t}-{\stackrel{⌢}{P}}_{H,t-1})-E_t({\stackrel{⌢}{P}}_{t+1}-{\stackrel{⌢}{P}}_t)=\rho (E_t{\stackrel{⌢}{C}}_{t+1}-{\stackrel{⌢}{C}}_t)& & (23)\end{array}$

Likewise for the foreign country, we must have:

$\begin{array}{ccc}\gamma ({\stackrel{⌢}{P}}_{\mathit{\text{Ft}}}^{*}-{\stackrel{⌢}{P}}_{F,t-1}^{*})-E_t({\stackrel{⌢}{P}}_{t+1}^{*}-{\stackrel{⌢}{P}}_t^{*})=\rho (E_t{\stackrel{⌢}{C}}_{t+1}^{*}-{\stackrel{⌢}{C}}_t^{*})& & (24)\end{array}$

From the usual linearization of the Calvo pricing equation and the home goods price index (9) around a path of zero inflation, in combination with the marginal cost definition (5) we have the forward-looking inflation equation given by:

$\begin{array}{ccc}{\stackrel{⌢}{P}}_{H,t}-{\stackrel{⌢}{P}}_{H,t-1}=1/\lambda (\rho {\stackrel{⌢}{C}}_t+{\stackrel{⌢}{P}}_t-{\stackrel{⌢}{P}}_{H,t}-{\stackrel{⌢}{A}}_t)+\beta E_t({\stackrel{⌢}{P}}_{H,t+1}-{\stackrel{⌢}{P}}_{H,t})& & (25)\end{array}$

where λ =κ/[(1 −κ)(1− βκ)] is a measure of the degree of price stickiness arising from the Calvo price-adjustment restriction. Likewise for the foreign country, we have

$\begin{array}{ccc}{\stackrel{⌢}{P}}_{F,t}^{*}-{\stackrel{⌢}{P}}_{F,t-1}^{*}=1/\lambda (\rho {\stackrel{⌢}{C}}_t^{*}+{\stackrel{⌢}{P}}_t^{*}-{\stackrel{⌢}{P}}_{F,t}^{*}-{\stackrel{⌢}{A}}_t^{*})+\beta E_t({\stackrel{⌢}{P}}_{F,t+1}^{*}-{\stackrel{⌢}{P}}_{F,t}^{*})& & (26)\end{array}$

Finally, a linear approximation of the home country goods market clearing condition (11) implies

$\begin{array}{ccc}{\stackrel{⌢}{Y}}_t=\mu {\stackrel{⌢}{C}}_t+(1-\mu ){\stackrel{⌢}{C}}_t^{*}-\theta \mu ({\stackrel{⌢}{P}}_{H,t}-{\stackrel{⌢}{P}}_t)-\theta (1-\mu )({\stackrel{⌢}{P}}_{H,t}-{\stackrel{⌢}{S}}_t-{\stackrel{⌢}{P}}_t^{*})& & (27)\end{array}$

We may re-write this system in terms of inflation and the terms of trade, using the definition ${\pi }_{H,t}={\stackrel{⌢}{P}}_{H,t}-{\stackrel{⌢}{P}}_{H,t-1}$ and ${\pi }_{F,t}={\stackrel{⌢}{P}}_{F,t}^{*}-{\stackrel{⌢}{P}}_{F,t-1}^{*}$ for domestic and foreign PPI inflation, respectively, and ${\tau }_t={\stackrel{⌢}{P}}_{F,t}^{*}+{\stackrel{⌢}{S}}_t-{\stackrel{⌢}{P}}_{H,t}$ for the home country terms of trade. Then we can use conditions (21)-(22) to reduce the model to a system of 6 equations in net foreign assets, consumption, inflation, home country output, and the terms of trade. The full system is described in Table 1.

Table 1.

Linear proximation of the model for given $\stackrel{⌢}{\alpha }$

Table 1.

Linear proximation of the model for given $\stackrel{⌢}{\alpha }$

Capital markets	$E_t({\stackrel{⌢}{C}}_{t+1}-{\stackrel{⌢}{C}}_t)=E_t({\stackrel{⌢}{C}}_{t+1}^{*}-{\stackrel{⌢}{C}}_t^{*})+(2\mu -1)E_t({\stackrel{⌢}{\tau }}_{t+1}-{\stackrel{⌢}{\tau }}_t)$
Budget constraint	$W_{t+1}=\frac{1}{\beta }{W}_t+{\stackrel{⌢}{Y}}_t-{\stackrel{⌢}{C}}_t-(1-\mu ){\stackrel{⌢}{\tau }}_t+{\stackrel{⌢}{\alpha }}^{\prime }{\stackrel{⌢}{r}}_{x,t}$
Home output	${\stackrel{⌢}{Y}}_t=\mu {\stackrel{⌢}{C}}_t+(1-\mu ){\stackrel{⌢}{C}}_t^{*}-\theta \mu ({\stackrel{⌢}{P}}_{H,t}-{\stackrel{⌢}{P}}_t)-\theta (1-\mu )({\stackrel{⌢}{P}}_{H,t}-{\stackrel{⌢}{S}}_t-\stackrel{⌢}{P}$
Home inflation	${\pi }_{H,t}={\lambda }^{-1}[\rho {\stackrel{⌢}{C}}_t+(1-\mu ){\stackrel{⌢}{\tau }}_t-u_t]+\beta E_t{\pi }_{H,t+1}$
Foreign inflation	${\pi }_{F,t}^{*}={\lambda }^{-1}[\rho {\stackrel{⌢}{C}}_t^{*}-(1-\mu ){\stackrel{⌢}{\tau }}_t-u_t^{*}]+\beta E_t{\pi }_{F,t+1}^{*}$
Home monetary rule	$\gamma {\pi }_{H,t}+m_t=E_t{\stackrel{⌢}{C}}_{t+1}-{\stackrel{⌢}{C}}_t+E_t[{\pi }_{H,t+1}+(1-\mu ){\stackrel{⌢}{\tau }}_{t+1}]$
Foreign monetary rule	$\gamma {\pi }_{F,t}^{*}+m_t^{*}=E_t{\stackrel{⌢}{C}}_{t+1}^{*}-{\stackrel{⌢}{C}}_t^{*}+E_t[{\pi }_{F,t+1}^{*}-(1-\mu ){\stackrel{⌢}{\tau }}_{t+1}]$

View Table

Table 1.

Linear proximation of the model for given $\stackrel{⌢}{\alpha }$

Capital markets	$E_t({\stackrel{⌢}{C}}_{t+1}-{\stackrel{⌢}{C}}_t)=E_t({\stackrel{⌢}{C}}_{t+1}^{*}-{\stackrel{⌢}{C}}_t^{*})+(2\mu -1)E_t({\stackrel{⌢}{\tau }}_{t+1}-{\stackrel{⌢}{\tau }}_t)$
Budget constraint	$W_{t+1}=\frac{1}{\beta }{W}_t+{\stackrel{⌢}{Y}}_t-{\stackrel{⌢}{C}}_t-(1-\mu ){\stackrel{⌢}{\tau }}_t+{\stackrel{⌢}{\alpha }}^{\prime }{\stackrel{⌢}{r}}_{x,t}$
Home output	${\stackrel{⌢}{Y}}_t=\mu {\stackrel{⌢}{C}}_t+(1-\mu ){\stackrel{⌢}{C}}_t^{*}-\theta \mu ({\stackrel{⌢}{P}}_{H,t}-{\stackrel{⌢}{P}}_t)-\theta (1-\mu )({\stackrel{⌢}{P}}_{H,t}-{\stackrel{⌢}{S}}_t-\stackrel{⌢}{P}$
Home inflation	${\pi }_{H,t}={\lambda }^{-1}[\rho {\stackrel{⌢}{C}}_t+(1-\mu ){\stackrel{⌢}{\tau }}_t-u_t]+\beta E_t{\pi }_{H,t+1}$
Foreign inflation	${\pi }_{F,t}^{*}={\lambda }^{-1}[\rho {\stackrel{⌢}{C}}_t^{*}-(1-\mu ){\stackrel{⌢}{\tau }}_t-u_t^{*}]+\beta E_t{\pi }_{F,t+1}^{*}$
Home monetary rule	$\gamma {\pi }_{H,t}+m_t=E_t{\stackrel{⌢}{C}}_{t+1}-{\stackrel{⌢}{C}}_t+E_t[{\pi }_{H,t+1}+(1-\mu ){\stackrel{⌢}{\tau }}_{t+1}]$
Foreign monetary rule	$\gamma {\pi }_{F,t}^{*}+m_t^{*}=E_t{\stackrel{⌢}{C}}_{t+1}^{*}-{\stackrel{⌢}{C}}_t^{*}+E_t[{\pi }_{F,t+1}^{*}-(1-\mu ){\stackrel{⌢}{\tau }}_{t+1}]$

This system contains the term ${\stackrel{⌢}{\alpha }}^{\prime }{\stackrel{⌢}{r}}_{x,t}$, which represents the wealth effects for the home country given an ex-post realization of excess returns, for an arbitrary portfolio holding. As noted before, up to a linear approximation, ${\stackrel{\swarrow }{r}}_{x,t}$ is a mean zero, i.i.d. variable. We may use this condition, and the definition of each asset in section 2 above, to compute the realization of ${\stackrel{⌢}{r}}_{x,t}$ for a given $\stackrel{⌢}{\alpha }$, using the solution to the system in Table 1. Without loss of generality, let the foreign nominal bond represent the residual asset N. Then the linearized vector of excess returns on home equity, foreign equity, and home nominal bonds is written as:

$\begin{array}{c}{\stackrel{⌢}{r}}_{x,1,t+1}=\beta {{\prod }}_{t+1}+(1-\beta ){\stackrel{⌢}{Z}}_{E,t+1}-E_t(\beta {{\prod }}_{t+1}+(1-\beta ){\stackrel{⌢}{Z}}_{E,t+1})\\ -({\stackrel{⌢}{Q}}_{t+1}-E_t{\stackrel{⌢}{Q}}_{t+1})+{\stackrel{⌢}{P}}_{t+1}^{*}-{\stackrel{⌢}{P}}_t^{*}-E_t({\stackrel{⌢}{P}}_{t+1}^{*}-{\stackrel{⌢}{P}}_t^{*})& & (28)\end{array}$

$\begin{array}{c}{\stackrel{⌢}{r}}_{x,2,t+1}=\beta {{\prod }}_{t+1}^{*}+(1-\beta ){\stackrel{⌢}{Z}}_{E,t+1}^{*}-E_t(\beta {{\prod }}_{t+1}^{*}+(1-\beta ){\stackrel{⌢}{Z}}_{E,t+1}^{*})\\ +{\stackrel{⌢}{P}}_{t+1}^{*}-{\stackrel{⌢}{P}}_t^{*}-E_t({\stackrel{⌢}{P}}_{t+1}^{*}-{\stackrel{⌢}{P}}_t^{*})& & (29)\end{array}$

$\begin{array}{ccc}{\stackrel{⌢}{r}}_{x,3,t+1}=-({\stackrel{⌢}{S}}_{t+1}-E_t{\stackrel{⌢}{S}}_{t+1})& & (30)\end{array}$

To compute ${\stackrel{⌢}{Z}}_{E,t}$, we use (6) and (7) applied to the pricing of home equity. This gives the change in the real price of equity as a function of the expected changes in the discounted sum of future real profits. In a similar way, we may compute ${\stackrel{⌢}{Z}}_{E,t}^{*}$.