## 1. Optimal Portfolio Shares of Foreign Equities

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---

### Introduction — role of portfolio choice in open macroeconomy
- In an open macroeconomy with asset trade, household portfolio choice may play an important role in understanding macro fluctuations.
- Representative agents in different countries may hold different portfolios depending on country-specific risks and returns.
- Lucas (1982) provides a fully optimizing portfolio-balance model (bonds, equities, claims to government monetary transfer) assuming complete nominal goods price flexibility.
- Models with sticky nominal goods prices are appropriate for considering real consequences of nominal exchange rate fluctuations.
- The equilibrium portfolio may depend importantly on short-run goods pricing behavior.

### Main contributions (selected)
- Contribution 1 (from supplied excerpt):
  - When there is a high degree of nominal goods price stickiness, the availability of a foreign-exchange hedge may play a key role in international risk sharing.
    - Model allows agents to trade equity shares and a forward position in foreign exchange.
    - There are real productivity shocks and nominal monetary shocks.
    - With this limited menu of assets, the equilibrium can mimic the complete markets outcome — real allocations are the same as if a complete set of nominal contingent claims were traded.
    - Portfolios that optimally spread risk may not exhibit much equity diversification.
    - If agents can diversify against risk arising from nominal exchange rate fluctuations, with sufficient nominal price stickiness, diversification in the equity portfolio need be minimal.
    - Equilibrium portfolios might exhibit home bias.
    - When equity portfolios are not diversified, shocks that affect relative consumption risk across countries operate through effects on relative prices — the real exchange rate and the terms of trade.
    - In the short run when nominal goods prices are sticky, much of that risk can be hedged on forward foreign exchange markets.
    - The foreign-exchange hedge requires that agents go long in their own currency and short in foreign currency.
    - The puzzle about international diversification may be about the foreign exchange denomination of nominal assets rather than the composition of the equity portfolio.
- Contribution 2 is listed in the source but not included in the supplied excerpt.

### Price stickiness and international asset choice — central insight
- Persistent productivity shocks drive real payoffs of assets; a priori price stickiness might seem minor for asset demands.
- Transitory nominal price stickiness can have a large impact on international portfolio choice because:
  - Under flexible goods prices, terms-of-trade and real exchange rate movements provide substantial automatic insurance for productivity shocks.
  - Under sticky nominal prices, those terms-of-trade adjustments cannot insure short-run shocks, making portfolio choice (equities vs. foreign hedges) the primary insurance mechanism even when price stickiness is transitory.
- Key consequence: When prices are sticky, the mix of home and foreign equities can differ dramatically from the flexible-price mix, even when prices adjust relatively rapidly.

### Static framework — complete hedging with a foreign-exchange forward
- Assumptions:
  - Two-country static model; representative household per country; goods imperfect substitutes; homothetic preferences; all nominal goods prices set ex ante.
  - Households initially endowed with ownership of domestic firms (equities not tradable) but can trade forward positions in foreign exchange prior to shocks.
- Main analytic results (static):
  - Relative consumption depends on the real exchange rate, relative goods prices, and asset payoffs (equation (8) and (9)).
  - The complete-markets allocation can be achieved if asset payoffs satisfy equation (11) (payoffs linear in real exchange rate and relative prices).
  - Under typical assumptions (law of one price, symmetric normalization), trading an instrument that hedges the terms of trade suffices (equation (12)).
  - With price stickiness (all nominal prices set ex ante), the log real exchange rate and terms of trade are linear in the log nominal exchange rate, so a forward position in foreign exchange can span the needed hedges.
  - Compact expression under partial pass-through assumptions: equation (13) gives κ = δ t_t s (text presents the formal definition of δ).
- Static portfolio equilibrium:
  - Ex ante zero-net-worth portfolios (long/short offset).
  - When agents can take the appropriate forward position, the model yields complete home bias in equity holdings: γ = 0 (no foreign equity holdings) in the static model (derivation culminating in equation (36) and substitution yielding 0γ=).
  - The optimal forward position in the static LCP case is given (equation (40) presented as "11 22 δ ρ =− +"); for 1ρ> the optimal δ is negative (Home agents are short in foreign currency).
  - Interpretation: with complete home bias (γ = 0) and an appropriate forward hedge, idiosyncratic risk is eliminated — conditional on the hedged exchange-rate risk, household consumption risk is non-diversifiable only through world consumption.

### Dynamic model — partial price stickiness, persistence, and portfolio formulas
- Setup:
  - Infinite-horizon model; fraction τ of firms set prices in advance each period; remaining firms can reoptimize.
  - Assets: Home and Foreign equities and forward foreign-exchange contracts.
  - Shocks: monetary and technology shocks (identical distributions across countries); allow correlation between monetary and technology shocks but not perfect correlation.
- Key analytic results (dynamic, linearized):
  - Complete markets condition replicated by spanning assets: c_t* - c_t = s_t + p_t - p_t* (text presents linearized form).
  - Forward position and equity share are constant over time in the linearized equilibrium:
    - Forward position: equation (67) — displayed formula in source for δ_t.
    - Foreign equity share in Home portfolio: equation (68) — displayed formula in source for γ_t with Λ and Ω defined explicitly there.
  - Interpretation of γ formula:
    - γ can be written as γ = FLEX * Λ + Ω (text phrase: "Our formula for the optimal share can be written as () FLEX γγ = ΛΛ+Ω, where FLEX γ is the share of foreign assets in the portfolio when prices are fully flexible.")
    - γ increases in Λ and decreases in Ω.
    - Condition for home bias (text reference to condition (69)).
  - Comparative statics and intuition:
    - γ is decreasing in τ when 1ω> (more price stickiness → greater home bias).
    - Labor’s share ζ amplifies bias direction: when home bias prevails, higher ζ increases home bias; when anti-home bias prevails, higher ζ increases foreign bias.
    - R β θ captures weight on the future and persistence of relative productivity shocks; larger R β θ shifts γ toward the flexible-price value.
    - When ω is close to one, terms-of-trade movements provide near-complete insurance under flexible prices; temporary price stickiness undermines that short-run insurance, making short-run portfolio choice more important.
  - Monetary policy neutrality for portfolio composition:
    - Equity and forward positions are unaffected by monetary policy changes because forward positions hedge monetary shocks; equity positions offset technology shocks orthogonal to exchange-rate risk.

### Calibrated portfolios — Table 1 selected outcomes and quantitative examples
- Calibration choices (text preserved verbatim):
  - "Following David K. Backus, Patrick J. Kehoe, and Finn E. Kydland (1992), we set 23ζ=."
  - "We follow Obstfeld and Rogoff (2003), and Paul R. Bergin (2006) and set 1ψ=."
  - Expected life of a nominal price in many calibrations is four quarters; paper considers τ in [0.05, 1] and maps period length so fraction τ equals four quarters.
  - Persistence and discount calibration: "The estimates of Backus, Kehoe, and Kydland (1992) give us on quarterly data that the autocorrelation of relative productivity shocks is 0.855, so we set 4/ (0.855) R τ θ = . Likewise, the quarterly discount factor in Backus et al. is 0.99, so we take 4/ (0.99) τ β = ."
  - Elasticity of substitution ω considered in a range from 1 up to 6: "In Table 2, we consider a range of values for ω, from 1 up to 6".
- Selected exact entries from Table 1 (optimal portfolio share of foreign equities γ):
  - τ=1.00: ω=1 → 0.00; ω=1.1 → 0.04; ω=1.5 → 0.14; ω=2 → 0.22; ω=3 → 0.31; ω=6 → 0.41.
  - τ=0.55: ω=1 → 0.00; ω=1.1 → 0.10; ω=1.5 → 0.38; ω=2 → 0.59; ω=3 → 0.84; ω=6 → 1.13.
  - τ=0.30: ω=1 → 0.00; ω=1.1 → 0.18; ω=1.5 → 0.60; ω=2 → 0.86; ω=3 → 1.09; ω=6 → 1.30.
  - τ=0.05: ω=1 → 0.00; ω=1.1 → 0.73; ω=1.5 → 1.24; ω=2 → 1.36; ω=3 → 1.43; ω=6 → 1.47.
- Quantitative interpretations from the source:
  - For ω = 1.5, the portfolio exhibits home bias as long as at least 40% of firms adjust prices with a lag (i.e., τ ≥ 0.40).
  - For ω = 1.1, when τ = 0.55, the share of foreign equities is 0.10.
  - For very large ω (e.g., ω = 6), the optimal portfolio tends to be biased toward foreign equities except when all firms have sticky prices.
- Source emphasis: Modest nominal price stickiness can imply large home bias in equity portfolios when households optimally use an exchange-rate hedge; complete-markets allocations can be replicated with very little equity diversification provided the appropriate foreign exchange hedge is taken.

### Policy-relevant conclusions and scenarios
- Availability and use of forward foreign-exchange hedges can substitute for equity diversification in achieving complete-markets allocations when nominal prices are sticky.
- Small amounts of nominal price rigidity (short-lived) can have large effects on equilibrium equity portfolios.
- Monetary policy (changes in money supply and in monetary response to technology) does not affect the equilibrium equity position or forward position because these are hedged via forward contracts; the equity position is determined by technology shock characteristics and price stickiness, holding money supplies constant.
- If nominal wages are sticky (alternative specification), households may optimally diversify more into foreign equities even with an exchange-rate hedge — wage stickiness increases the diversification needed.
- Currency of price setting (LCP, PCP, exchange-rate indexing) affects the forward position but not the equity position provided households can freely hedge exchange-rate risk.
- Empirical implication: countries’ net foreign-exchange positions (forward/nominal asset positions), not insufficient equity diversification, may explain failures of complete risk sharing observed in data; suboptimal forward positions could be the culprit.

*Excerpt and results drawn verbatim from the IMF Working Paper chapter "_wp0912 - 1. Optimal Portfolio Shares of Foreign Equities" and "_wp0912 - 2. It might seem that price stickiness should be a minor consideration for asset demands."*

### 1. Optimal Portfolio Shares of Foreign Equities......................................................................32

### 1. Optimal Portfolio Shares of Foreign Equities

### I. INTRODUCTION — role of portfolio choice in open macroeconomy
- In an open macroeconomy in which asset trade is possible, the portfolio choice of households may play an important role in understanding macro fluctuations.
- In contrast to a closed economy model–in which a representative agent simply holds the market portfolio–agents in each country may hold different portfolios depending on the country-specific risks and returns that they encounter.
- Robert E. Lucas (1982) provides a fully optimizing model of portfolio balance, in which households trade bonds, equities, and claims to monetary transfer from the government.
- Lucas (1982) and subsequent fully-worked out portfolio-balance models have assumed complete nominal goods price flexibility.
- Models with sticky nominal goods prices might be appropriate for the consideration of the real consequences of nominal exchange rate fluctuations.
- The paper shows that the equilibrium portfolio may depend in important ways on short-run goods pricing behavior.

### Main contributions
- The paper makes two main contributions:
  1. When there is a high degree of nominal goods price stickiness, the availability of a foreign-exchange hedge may play a key role in international risk sharing.
     - The model considered allows agents to trade equity shares and a forward position in foreign exchange.
     - There are real productivity shocks and nominal monetary shocks in the model.
     - With this limited menu of assets, the equilibrium mimics the complete markets outcome–real allocations are the same as if a complete set of nominal contingent claims were traded.
     - However, the portfolios that optimally spread risk may not exhibit much equity diversification.
     - If agents can diversify against risk arising from nominal exchange rate fluctuations, with sufficient nominal price stickiness, diversification in the equity portfolio need be minimal.
     - Equilibrium portfolios might exhibit home bias.
     - The shocks that affect relative consumption risk across countries operate through their effects on relative prices–the real exchange rate and the terms of trade–when equity portfolios are not diversified.
     - In the short run when nominal goods prices are sticky, much of that risk can be hedged on forward foreign exchange markets.
     - Put differently, when goods prices are sticky, it is not the equity portfolio that bears most of the burden of risk sharing, but rather the foreign exchange position.
     - The optimal exchange-rate hedge requires that agents go long in their own currency and short in foreign currency.
     - The real puzzle about international diversification may turn out to be about the foreign exchange denomination of nominal assets in international portfolios rather than the composition of the equity portfolio.
  2. (Contribution 2 is listed but not included in the supplied content excerpt.)

*Source: _wp0912 - 1. Optimal Portfolio Shares of Foreign Equities (selected excerpt)*

### 2. It might seem that price stickiness should be a minor consideration for asset demands.

### _wp0912 - 2. It might seem that price stickiness should be a minor consideration for asset demands.

### Price stickiness and international asset choice — central insight
- Persistent productivity shocks drive real payoffs of assets; a priori one might expect price stickiness to have only a small effect on expected present value of assets.
- Transitory nominal price stickiness can have a large impact on international portfolio choice because:
  - Under flexible goods prices, terms-of-trade and real exchange rate movements provide substantial automatic insurance for productivity shocks.
  - Under sticky nominal prices, those terms-of-trade adjustments cannot insure short-run shocks, making portfolio choice (equities vs. foreign hedges) the primary insurance mechanism even when price stickiness is transitory.
- Key consequence: When prices are sticky, the mix of home and foreign equities can differ dramatically from the flexible-price mix, even when prices adjust relatively rapidly.

### Static framework — complete hedging with a foreign-exchange forward
- General static two-country model assumptions:
  - Representative household per country; goods are imperfect substitutes; homothetic preferences; all nominal goods prices set ex ante.
  - Households are initially endowed with ownership of domestic firms (equities not tradable) but can trade forward positions in foreign exchange prior to shocks.
- Main analytic results (static):
  - Relative consumption depends on the real exchange rate, relative goods prices, and asset payoffs (equation (8) and (9)).
  - The complete-markets allocation can be achieved if asset payoffs satisfy equation (11) (payoffs linear in real exchange rate and relative prices).
  - Under typical assumptions (law of one price, symmetric normalization), trading an instrument that hedges the terms of trade suffices (equation (12)).
  - With price stickiness (all nominal prices set ex ante), the log real exchange rate and terms of trade are linear in the log nominal exchange rate, so a forward position in foreign exchange can span the needed hedges.
  - Specific compact expression under partial pass-through assumptions: equation (13) gives κ = δ t_t s (presented as "tt s κ δ = ," followed by the formal definition of δ). The paper notes that if Home and Foreign agents take the forward position δ units, the complete-markets allocation obtains.
- Static portfolio equilibrium:
  - Ex ante zero-net-worth portfolios (long/short offset).
  - When agents can take the appropriate forward position, the model yields complete home bias in equity holdings: γ = 0 (no foreign equity holdings) in the static model (derivation culminating in equation (36) and substitution yielding 0γ=).
  - The optimal forward position in the static LCP case is given (equation (40) presented as "11 22 δ ρ =− +"), and the text emphasizes that for 1ρ> the optimal δ is negative (Home agents are short in foreign currency).
  - Interpretation: with complete home bias ( γ = 0 ) and an appropriate forward hedge, idiosyncratic risk is eliminated — conditional on the hedged exchange-rate risk, household consumption risk is non-diversifiable only through world consumption.

### Dynamic model — partial price stickiness, persistence, and portfolio formulas
- Model setup highlights:
  - Infinite-horizon model, fraction τ of firms set prices in advance each period; remaining firms can reoptimize.
  - Assets: Home and Foreign equities and forward foreign-exchange contracts.
  - Shocks: monetary and technology shocks (identical distributions across countries); allow correlation between monetary and technology shocks but not perfect correlation.
- Key analytic results (dynamic):
  - With complete markets replicated by the spanning assets, the complete-markets condition (equation (66)) holds in linearized form: **c_t* - c_t = s_t + p_t - p_t*** (presented as "**() tt    t  t  t cc  s p pρ−=+ −.**" in the text).
  - Forward position and equity share are constant over time in the linearized equilibrium:
    - Forward position: equation (67) — "11 1 2 t δ δ τ ρ ⎛⎞ ≡ = − ⎜⎟ ⎝⎠" (presented in text as the exact displayed formula).
    - Foreign equity share in Home portfolio: equation (68) — " *1 2(1) tt γγ γ ζ Λ ≡ == −Ω+Λ " with Λ and Ω defined explicitly in text (full expressions preserved verbatim there).
  - Interpretation of γ formula:
    - γ decomposed as γ = FLEX * Λ + Ω (text phrase: "Our formula for the optimal share can be written as () FLEX γγ = ΛΛ+Ω, where FLEX γ is the share of foreign assets in the portfolio when prices are fully flexible.")
    - γ increases in Λ and decreases in Ω.
    - For home bias (1/2 γ <), condition (69) must hold (presented verbatim in text).
  - Comparative statics and intuition:
    - γ is decreasing in τ when 1ω> (more price stickiness → greater home bias).
    - Labor’s share ζ amplifies the direction of bias (when home bias prevails, higher ζ increases home bias; when anti-home bias prevails, higher ζ increases foreign bias).
    - R β θ captures weight on the future and persistence of relative productivity shocks; larger R β θ shifts γ toward the flexible-price value.
    - Terms-of-trade insurance under flexible prices: when ω is close to one, terms-of-trade movements provide near-complete insurance, reducing gains from equity diversification; temporary price stickiness undermines that short-run insurance, making the short-run portfolio choice more important.
  - Monetary policy neutrality for portfolio composition:
    - Equity and forward positions are unaffected by monetary policy changes because forward positions hedge monetary shocks; equity positions offset technology shocks orthogonal to exchange-rate risk.

### Calibrated portfolios — Table 1 outcomes and quantitative examples
- Parameter choices and calibrations used in the paper (exact text preserved):
  - "Following David K. Backus, Patrick J. Kehoe, and Finn E. Kydland (1992), we set 23ζ=."
  - "We follow Obstfeld and Rogoff (2003), and Paul R. Bergin (2006) and set 1ψ=."
  - Expected life of a nominal price in many calibrations is four quarters; paper considers τ in [0.05, 1] and maps period length so fraction τ equals four quarters.
  - Persistence and discount calibration: "The estimates of Backus, Kehoe, and Kydland (1992) give us on quarterly data that the autocorrelation of relative productivity shocks is 0.855, so we set 4/ (0.855) R τ θ = . Likewise, the quarterly discount factor in Backus et al. is 0.99, so we take 4/ (0.99) τ β = ."
  - Elasticity of substitution ω considered in a range from 1 up to 6 (text: "In Table 2, we consider a range of values for ω, from 1 up to 6").
- Table 1 (optimal portfolio share of foreign equities) — selected exact entries (table presented in the source):
  - Row headers τ values and column headers ω values; entries are the calculated γ values. Examples taken verbatim from Table 1:
    - τ=1.00: ω=1 → 0.00; ω=1.1 → 0.04; ω=1.5 → 0.14; ω=2 → 0.22; ω=3 → 0.31; ω=6 → 0.41.
    - τ=0.55: ω=1 → 0.00; ω=1.1 → 0.10; ω=1.5 → 0.38; ω=2 → 0.59; ω=3 → 0.84; ω=6 → 1.13.
    - τ=0.30: ω=1 → 0.00; ω=1.1 → 0.18; ω=1.5 → 0.60; ω=2 → 0.86; ω=3 → 1.09; ω=6 → 1.30.
    - τ=0.05: ω=1 → 0.00; ω=1.1 → 0.73; ω=1.5 → 1.24; ω=2 → 1.36; ω=3 → 1.43; ω=6 → 1.47.
- Qualitative quantitative interpretation given in source:
  - For ω = 1.5, the portfolio exhibits home bias as long as at least 40% of firms adjust prices with a lag (i.e., τ ≥ 0.40).
  - For ω = 1.1, when τ = 0.55, the share of foreign equities is only 10% (table entry τ=0.55, ω=1.1 = 0.10).
  - For very large ω (e.g., ω = 6), the optimal portfolio tends to be biased toward foreign equities except when all firms have sticky prices.
- Source interpretation emphasized in text:
  - The calibrated table illustrates that modest nominal price stickiness can imply large home bias in equity portfolios when households optimally use an exchange-rate hedge; the complete-markets allocation can be replicated with very little equity diversification provided the appropriate foreign exchange hedge is taken.

### Policy-relevant conclusions and scenarios
- Policy/practical implications (as stated in the source text, preserved in meaning and equation references):
  - Availability and use of forward foreign-exchange hedges can substitute for equity diversification in achieving complete-markets allocations when nominal prices are sticky.
  - Small amounts of nominal price rigidity (short-lived) can have large effects on equilibrium equity portfolios.
  - Monetary policy (changes in money supply and in monetary response to technology) does not affect the equilibrium equity position or forward position because these are hedged via forward contracts; the equity position is determined by technology shock characteristics and price stickiness, holding money supplies constant.
  - If nominal wages are sticky (alternative specification), households may optimally diversify more into foreign equities even with an exchange-rate hedge — wage stickiness increases the diversification needed to achieve complete-markets allocations.
  - Currency of price setting (LCP, PCP, exchange-rate indexing) affects the forward position but not the equity position provided households can freely hedge exchange-rate risk.
  - Empirical puzzle on incomplete risk sharing: the paper suggests that countries’ net foreign-exchange positions (forward/nominal asset positions), not insufficient equity diversification, may explain failures of complete risk sharing observed in data; i.e., suboptimal forward positions could be the culprit.

*Italic source attribution: Excerpt and results drawn verbatim from the IMF Working Paper chapter "_wp0912 - 2. It might seem that price stickiness should be a minor consideration for asset demands."*

### REFERENCES

### _wp0912 - REFERENCES

### International real business cycles, trade balance, and exchange rates
- Backus, David K., Patrick J. Kehoe, and Finn E. Kydland, 1992, “International Real Business Cycles,” Journal of Political Economy, Vol. 100, No. 4, pp. 745-75.
- –––––, 1994, “Dynamics of the Trade Balance and the Terms of Trade: The J-Curve?” American Economic Review, Vol. 84, No. 1, pp. 84-103.
- Lucas, Robert E., 1982, “Interest Rates and Currency Prices in a Two-Country World,” Journal of Monetary Economics, Vol. 10, No. 3, pp. 335-59.
- Chari, V. V., Patrick J. Kehoe, and Ellen R. McGrattan, 2002, “Can Sticky Price Models Generate Volatile and Persistent Real Exchange Rates?” Review of Economic Studies, Vol. 69, No. 3, pp. 533-63.
- Bergin, Paul R, 2006, “How Well Can the New Open Economy Macroeconomics Explain the Exchange Rate and the Current Account?” Journal of International Money and Finance, Vol. 25, No.5, pp. 675-701.
- Obstfeld, Maurice, 2007, “International Risk Sharing and the Costs of Trade,” Ohlin Lectures, Stockholm School of Economics. http://elsa.berkeley.edu/~obstfeld/Ohlin_show.pdf.
- Obstfeld, Maurice, and Kenneth Rogoff, 1996, Foundations of International Macroeconomics. Cambridge, MA: MIT Press.
- Obstfeld, Maurice, 2003, “Risk and Exchange Rates,” in Contemporary Economic Policy: Essays in Honor of Assaf Razin, Elhanan Helpman and Effraim Sadka (eds.). Cambridge: Cambridge University Press.
- Tille, Cedric, and Eric van Wincoop, 2008b, “A New Perspective on ‘The New Rule’ of the Current Account.” http://www.people.virginia.edu/~ev4n/papers/kraay_June_27.pdf.

### International diversification, portfolio choice, and home bias
- Baxter, Marianne, and Urban J. Jermann, 1997, “The International Diversification Puzzle Is Worse Than You Think,” American Economic Review, Vol. 87, No.1, pp. 170-80.
- Bottazzi, Laura, Paolo Pesenti, and Eric van Wincoop, 1996, “Wages, Profits and the International Portfolio Puzzle,” European Economic Review, Vol. 40, No. 2, pp. 219-54.
- Cole, Harold L., and Maurice Obstfeld, 1991, “Commodity Trade and International Risksharing: How Much Do Financial Markets Matter?” Journal of Monetary Economics, Vol. 28, No. 1, pp. 3-24.
- French, Kenneth R., and James M. Poterba, 1991, “Investor Diversification and International Equity Markets,” American Economic Review, Vol. 81, No. 2, pp. 222-26.
- Heathcote, Jonathan, and Fabrizio Perri, 2002, “Financial Autarky and International Business Cycles,” Journal of Monetary Economics, Vol. 49, No. 3, pp. 601-27.
- Heathcote, Jonathan, and Fabrizio Perri, 2008, “The International Diversification Puzzle is not as Bad as You Think.” http://www9.georgetown.edu/faculty/jhh9/homebias.pdf.
- Jermann, Urban J., 2002, “International Portfolio Diversification and Endogenous Labor Supply Choice,” European Economic Review, Vol. 46, No.3, pp. 507-22.
- Julliard, Christian, 2002, “The International Diversification Puzzle is Not Worse than You Think.” Unpublished.
- Julliard, Christian, 2004, “Human Capital and International Portfolio Choice.” http://personal.lse.ac.uk/julliard/papers/IPD.pdf.
- Lewis, Karen K., 1999, “Trying to Explain Home Bias in Equities and Consumption,” Journal of Economic Literature, Vol. 37, No. 2, pp. 571-608.
- Lewis, Karen K., 2000, “Why Do Stocks and Consumption Imply Such Different Gains from International Risk Sharing?” Journal of International Economics, Vol. 52, No.1, pp. 1-35.
- Palacios-Huerta, Ignacio, 2001, “The Human Capital of Stockholders and the International Diversification Puzzle,” Journal of International Economics, Vol. 54, No. 2, pp. 309-31.
- Pesenti, Paolo, and Eric van Wincoop, 2002, “Can Nontradables Generate Substantial Home Bias?” Journal of Money, Credit, and Banking, Vol. 34, No.1, pp. 25-50.
- Warnock, Francis E., 2002, “Home Bias and High Turnover Reconsidered,” Journal of International Money and Finance, Vol. 21, No. 6, pp. 795-805.
- Tesar, Linda L., 1993, “International Risk-Sharing and Nontraded Goods,” Journal of International Economics, Vol. 35, No. 1/2, pp. 69-89.
- Tesar, Linda L., and Ingrid M. Werner, 1995, “Home Bias and High Turnover,” Journal of International Money and Finance, Vol.14, No. 4, pp. 467-92.
- Bottazzi, Laura, Paolo Pesenti, and Eric van Wincoop, 1996, “Wages, Profits and the International Portfolio Puzzle,” European Economic Review, Vol. 40, No. 2, pp. 219-54.

### Nontraded goods, nontraded factors, and macro pricing
- Baxter, Marianne, and Robert G. King, 1998, “Nontraded Goods, Nontraded Factors, and International Non-Diversification,” Journal of International Economics, Vol. 44, No. 2, pp. 211-29.
- Tesar, Linda L., 1993, “International Risk-Sharing and Nontraded Goods,” Journal of International Economics, Vol. 35, No. 1/2, pp. 69-89.
- Pesenti, Paolo, and Eric van Wincoop, 2002, “Can Nontradables Generate Substantial Home Bias?” Journal of Money, Credit, and Banking, Vol. 34, No.1, pp. 25-50.
- Engel, Charles, 2006, “Equivalence Results for Optimal Pass-Through, Optimal Indexing to Exchange Rates, and Optimal Choice of Currency for Export Pricing,” Journal of the European Economics Association, Vol. 4, No. 6, pp.1249-260.
- Blanchard, Olivier Jean, and Nobuhiro Kiyotaki, 1987, “Monopolistic Competition and the Effects of Aggregate Demand.” American Economic Review, Vol. 77, No. 4, pp. 647-66.
- Taylor, John B., 1999, “Staggered Price and Wage Setting in Macroeconomics,” in Handbook of Macroeconomics. Vol. 1, John B. Taylor and Michael Woodford (eds.), pp. 1009-050. Amsterdam: Elsevier.

### Valuation effects, net external assets, and capital flows
- Devereux, Michael B., and Alan Sutherland, 2006, “Solving for Country Portfolios in Open Economy Macro Models,” Centre for Economic Policy Research Discussion Papers 5966.
- Devereux, Michael B., and Alan Sutherland, 2007, “Country Portfolio Dynamics,” Centre for Economic Policy Research Discussion Papers 6208.
- Devereux, Michael B., and Alan Sutherland, 2008, “Valuation Effects and the Dynamics of Net External Assets.” Paper presented at the IMF-ESRC-WEF conference on International Macro-Finance.
- Devereux, Michael B., and Alan Sutherland, forthcoming, “Financial Globalization and Monetary Policy.” Journal of Monetary Economics.
- Tille, Cedric, and Eric van Wincoop, 2008a, “International Capital Flows,” http://www.people.virginia.edu/~ev4n/papers/capflows_Apr_18.pdf.
- Lustig, Hanno, and Stijn van Nieuwerburgh, 2008, “The Returns on Human Wealth: Good News on Wall Street is Bad News on Main Street,” Review of Financial Studies, Vol. 21, No. 5, pp. 2097-137.

### Methods, numerical solutions, and technical contributions
- Evans, Martin D.D., and Viktoria Hnatkovska, 2008, “A Method for Solving General Equilibrium Models with Incomplete Markets and Many Financial Assets,” http://www.econ.ubc.ca/vhnatkovska/Research/solumethod_Evans_Hnatkovska.pdf
- Devereux, Michael B., and Alan Sutherland, 2006, “Solving for Country Portfolios in Open Economy Macro Models,” Centre for Economic Policy Research Discussion Papers 5966.
- Devereux, Michael B., and Alan Sutherland, 2007, “Country Portfolio Dynamics,” Centre for Economic Policy Research Discussion Papers 6208.
- Julliard, Christian, 2004, “Human Capital and International Portfolio Choice.” http://personal.lse.ac.uk/julliard/papers/IPD.pdf.
- Matsumoto, Akito, 2004, “Essays in International Finance,” PhD diss., University of Wisconsin.
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*References as listed in _wp0912 - REFERENCES*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp0912.pdf_