International Portfolios, Capital Accumulation and Foreign Asset Dynamics N. Coeurdacier, R. Kollman and P. Martin Discussion Sumru Altug Koç University and CEPR 8th Macroeconomic Policy Research Workshop on DSGE Models September 3-4, 2009 Budapest, Hungary Magyar Nemzeti Bank and CEPR

Introduction This paper integrates International Real Business Cycle (IRBC) theory with the literature on international capital flows The paper analyzes the issue of equity home bias using an IRBC model with multi-asset portfolios of equities and bonds It matches standard business cycle moments and also examines the dynamics of external asset positions.

The Setup 2 country, 2 good IRBC model The good in each country can be used for consumption and investment in home and foreign goods. There are TFP shocks and shocks to the marginal efficiency of investment (MEI). There is also international trade in stocks and bonds. There is home bias in the composition of consumption and investment goods.

Results The portfolios of equities and bonds are able to support the complete markets allocations across countries or full risk sharing. The equity home bias is derived solely from the local bias in investment spending and does not depend on the elasticity of substitution between home and foreign goods. Terms of trade shocks are in turn hedged by the bond portfolio.

Analytics The paper makes use of zero-order portfolios along the lines of Devereux and Sutherland (2006a,b). These are portfolio decision rules evaluated at the steady values of the state variables. The notion is to find restrictions on zero-order portfolios of equities and bonds such that a linearized version of the full risk sharing condition holds – namely, that the ratio of the marginal utilities of aggregate consumption equal to the consumption-based real exchange rate, P HT /P FT, where P it denotes the price index for country i. Let S denote the country’s holdings of local stock and b its holdings of local bonds.

Analytics (cont.’d) The linearized budget constraint for country i is given by P it C it = w it l it + Sd it +(1-S)d it +b(p it -p jt ), i=H,F, where p it denotes the price of good i. Next subtract the static budget constraint of country F from that of country H. Linearizing the resulting equation, substituting for the full risk sharing condition and for the relative wage income and relative dividends in terms of relative investment and the terms of trade yields expressions for local equity holdings and local bond holdings relative to GDP which display the main results of the paper (equations 31 and 32).

Intuition When there is a local bias towards investment spending, a Home investment boom leads to a decline in Home dividends and a rise in Home output and Home labor income. Thus, the equity home bias arises as local equities are used to hedge against movements in local wage income. The key point is note that such movements in local dividends and the local wage income are assumed to be at constant terms of trade, which does not alter the countries’ relative consumption under efficient risk sharing. Terms of trade changes are then hedged through the bonds portfolio, as the terms of trade movements are perfectly correlated with the difference between the payoffs on Home versus Foreign good bonds.

Related Literature Heathcote and Perri (2007) obtained equity home bias for a unit elasticity of substitution (ES) between home and foreign goods and log utility. They assumed only TFP shocks and no bond market. The current paper generalizes the results of Heathcote and Perri (2007) to CRRA utility and unrestricted ES by allowing for a bond market and shocks to the MEI. See also Collard, Dellas, Diba and Stockman (2007).

Related Literature Engel and Matsumoto (2006) analyze international equity choices in a model with money, sticky prices, and nominal bonds (but no capital accumulation). With price stickiness, a positive productivity shock leads to a decline in employment and output and an increase in profits. Hence, equities are an effective hedge against labor income risk, conditional on the nominal exchange rate. The current paper derives a similar result without resorting to price stickiness.

Measuring Equity Returns Dividends in the model are obtained by subtracting gross investment from profits Is this a good proxy for equity returns? The results of the paper emphasize the conditional covariance between relative wage income and dividends. Based on these proxies, the paper argues that the relevant conditional covariance is negative in the data. Following Couerdacier and Gourinchas (2009), one can examine the conditional covariance between equity returns and the returns to human capital. There is less evidence that is negative, especially for Eurozone countries.

Implications for Bond Holdings Calibration assumes that the elasticities of substitution in consumption and investment are greater than unity. This leads to the Home country going long on its own bonds. (See pages 14 and 23.) Under the model’s calibration, a terms of trade deterioration caused by a productivity shock is associated with the country going long on its own bonds. Yet this may not be consistent with many developed economies’ experiences (US?).

IRBC Puzzles The quantity anomaly: In the data, the cross-country correlations of output exceed those of consumption whereas due to full risk-sharing, these are reversed in the model. The presence of MEI shocks lowers the cross-country correlation of consumption to be consistent with the data but also cause the cross-country correlations of output and investment to be too low. The price anomaly: Standard IRBC models sharply under-predict the volatility of the real exchange rate. With MEI shocks in addition to TFP shocks, model performs better in this dimension but still cannot match the data.

Implications for Capital Flows The strength of the paper is in incorporating international portfolio choices into the IRBC model. The correlation properties of NFA and of equity and debt holdings appears to be driven by the properties of the model (full risk sharing). Limited participation in equity markets, borrowing constraints, informational considerations not considered when trying to account for the behavior of international portfolio flows.

Conclusion Richer framework relative to the literature that allows for joint consideration of real outcomes and asset market phenomena Provides headway in addressing asset market dynamics Suffers from the inability to address some key IRBC puzzles Methodological question: How should we move forward? The approach of matching the model “moment by moment”: as we fix one “moment”, performance deteriorates for another “moment”.

Conclusion Different models have strengths in addressing one phenomena but are silent on others. GHH preferences may be useful for increasing, say, the consumption-investment correlation but they may also alter the results on equity home bias. Limited enforcement models along the lines of Kehoe and Perri (2002) are successful in addressing many of the IRBC puzzles. However, they have not been modified to account for international portfolio choices directly. More generally, how can we model the role of incomplete markets? In the current paper, the model is effectively complete because the state space generated by two shocks is spanned by home and foreign equities and real bonds. How could we “test” for such spanning using information on real allocations and capital flows? Another approach is to assume complete markets but allow for costs of participation in financial markets, borrowing constraints as in Luttmer (1999), JF.