Aiyagari, S. R. (1994): “Uninsured Idiosyncratic Risk and Aggregate Saving,” The Quarterly Journal of Economics, 109(3), 659–684.
Backus, D. K., P. J. Kehoe, and F. E. Kydland (1992): “International Real Business Cycles,” Journal of Political Economy, 100(4), 745–775.
Backus, D. K., and G. W. Smith (1993): “Consumption and real exchange rates in dynamic economies with non-traded goods,” Journal of International Economics, 35(34), 297–316.
Baxter, M., and U. J. Jermann (1997): “The International Diversification Puzzle Is Worse Than You Think,” The American Economic Review, 87(1), 170–180.
Benetrix, A. S., P. R. Lane, and J. C. Shambaugh (2015): “International currency exposures, valuation effects and the global financial crisis,” Journal of International Economics, 96(Supplement 1), S98-S109.
Benigno, G., and C. Thoenissen (2008): “Consumption and real exchange rates with incomplete markets and non-traded goods,” Journal of International Money and Finance, 27(6), 926–948.
Benigno, P. (2009): “Are valuation effects desirable from a global perspective?,” Journal of Development Economics, 89(2), 170–180.
Berriel, T. C., and S. Bhattarai (2013): “Hedging Against the Government: A Solution to the Home Asset Bias Puzzle,” American Economic Journal: Macroeconomics, 5(1), 102–134.
Burnside, C., M. Eichenbaum, I. Kleshchelski, and S. Rebelo (2011): “Do Peso Problems Explain the Returns to the Carry Trade?,” Review of Financial Studies, 24(3), 853–891.
Cavallo, M., and C. Tille (2006): “Current account adjustment with high financial integration: a scenario analysis,” Economic Review, pp. 31–45.
Chari, V. V., P. J. Kehoe, and E. R. McGrattan (2002): “Can Sticky Price Models Generate Volatile and Persistent Real Exchange Rates?,” The Review of Economic Studies, 69(3), 533–563.
Coeurdacier, N., and P.-O. Gourinchas (2016): “When bonds matter: Home bias in goods and assets,” Journal of Monetary Economics, 82(Supplement C), 119–137.
Coeurdacier, N., R. Kollmann, and P. Martin (2010): “International portfolios, capital accumulation and foreign assets dynamics,” Journal of International Economics, 80(1), 100–112.
Coeurdacier, N., and H. Rey (2013): “Home Bias in Open Economy Financial Macroeconomics,” Journal of Economic Literature, 51(1), 63–115.
Colacito, R., and M. M. Croce (2013): “International Asset Pricing with Recursive Preferences,” The Journal of Finance, 68(6), 2651–2686.
Corsetti, G., L. Dedola, and S. Leduc (2008): “International Risk Sharing and the Transmission of Productivity Shocks,” The Review of Economic Studies, 75(2), 443–473.
Corsetti, G., L. Dedola, and S. Leduc (2014): “The International Dimension of Productivity and Demand Shocks in the Us Economy,” Journal of the European Economic Association, 12(1), 153–176.
Devereux, M. B., and A. Sutherland (2007): “Monetary Policy and Portfolio Choice in an Open Economy Macro Model,” Journal of the European Economic Association, 5(2–3), 491–499.
Devereux, M. B., and A. Sutherland (2010): “Country portfolio dynamics,” Journal of Economic Dynamics and Control, 34(7), 1325–1342.
Devereux, M. B., and A. Sutherland (2011): “Country Portfolios in Open Economy Macro-Models,” Journal of the European Economic Association, 9(2), 337–369.
Devereux, M. B., and J. Yetman (2010): “Leverage constraints and the international transmission of shocks,” Journal of Money, Credit and Banking, 42(s1), 71–105.
Eichengreen, B., R. Hausmann, and U. Panizza (2003): “The pain of original sin,” Other Peoples Money: Debt Denomination and Financial Instability in Emerging Market Economies, pp. 1–49.
Engel, C. (1996): “The forward discount anomaly and the risk premium: A survey of recent evidence,” Journal of Empirical Finance, 3(2), 123–192.
Engel, C. M., and A. Matsumoto (2009): “International Risk Sharing: Through Equity Diversification or Exchange Rate Hedging?,” SSRN Scholarly Paper ID 1438847, Social Science Research Network, Rochester, NY.
Evans, M. D. D., and V. Hnatkovska (2012): “A method for solving general equilibrium models with incomplete markets and many financial assets,” Journal of Economic Dynamics and Control, 36(12), 1909–1930.
Evans, M. D. D., and V. V. Hnatkovska (2014): “International capital flows, returns and world financial integration,” Journal of International Economics, 92(1), 14–33.
Feenstra, R. C., R. Inklaar, and M. P. Timmer (2015): “The next generation of the Penn World Table,” The American Economic Review, 105(10), 3150–3182.
Fernndez-Villaverde, J., J. F. Rubio-Ramrez, and F. Schorfheide (2016): “Chapter 9 - Solution and Estimation Methods for DSGE Models,” in Handbook of Macroeconomics, ed. by J. B. T. a. H. Uhlig, vol. 2, pp. 527–724. Elsevier, DOI: 10.1016/bs.hesmac.2016.03.006.
- Search Google Scholar
- Export Citation
)| false ( Fernndez-Villaverde, J., J. F. Rubio-Ramrez, and F. Schorfheide 2016): “Chapter 9 - Solution and Estimation Methods for DSGE Models,” in Handbook of Macroeconomics, ed. by , vol. J. B. T. a. H. Uhlig 2, pp. 527– 724. Elsevier, DOI: 10.1016/bs.hesmac.2016.03.006.
Gourinchas, P.-O., and H. Rey (2014): “External Adjustment, Global Imbalances, Valuation Effects,” Handbook of International Economics, 4, 585–645.
Heathcote, J., and F. Perri (2002): “Financial autarky and international business cycles,” Journal of Monetary Economics, 49(3), 601–627.
Huggett, M. (1993): “The risk-free rate in heterogeneous-agent incomplete-insurance economies,” Journal of Economic Dynamics and Control, 17(5), 953–969.
Karabarbounis, L. (2014): “Home production, labor wedges, and international business cycles,” Journal of Monetary Economics, 64, 68–84.
Lane, P. R., and J. C. Shambaugh (2010a): “Financial Exchange Rates and International Currency Exposures,” The American Economic Review, 100(1), 518–540.
Lane, P. R., and J. C. Shambaugh (2010b): “The long or short of it: Determinants of foreign currency exposure in external balance sheets,” Journal of International Economics, 80(1), 33–44.
Lee, J., F. Ghironi, and A. Rebucci (2009): “The Valuation Channel of External Adjustment,” IMF Working Papers 09/275, International Monetary Fund.
Lucas Jr., R. E. (1982): “Interest rates and currency prices in a two-country world,” Journal of Monetary Economics, 10(3), 335–359.
Lustig, H., and A. Verdelhan (2016): “Does Incomplete Spanning in International Financial Markets Help to Explain Exchange Rates?,” Working Paper.
Maliar, L., and S. Maliar (2015): “Merging simulation and projection approaches to solve high-dimensional problems with an application to a new Keynesian model,” Quantitative Economics, 6(1), 1–47.
Matsumoto, A., and C. Engel (2009): The international diversification puzzle when goods prices are sticky: it's really about exchange-rate hedging, not equity portfolios, no. 9–12. International Monetary Fund.
Mendoza, E., V. Quadrini, and J. R iosRull (2009): “Financial Integration, Financial Development, and Global Imbalances,” Journal of Political Economy, 117(3), 371–416.
Menkhoff, L., L. Sarno, M. Schmeling, and A. Schrimpf (2012): “Carry Trades and Global Foreign Exchange Volatility,” The Journal of Finance, 67(2), 681–718.
Rabitsch, K., S. Stepanchuk, and V. Tsyrennikov (2015): “International portfolios: A comparison of solution methods,” Journal of International Economics, 97(2), 404–422.
Schmitt-Grohe, S., and M. Uribe (2003): “Closing small open economy models,” Journal of International Economics, 61(1), 163–185.
Stockman, A. C., and L. L. Tesar (1995): “Tastes and Technology in a Two-Country Model of the Business Cycle: Explaining International Comovements,” The American Economic Review, 85(1), 168–185.
Tille, C. (2008): “Financial integration and the wealth effect of exchange rate fluctuations,” Journal of International Economics, 75(2), 283–294.
Any asset with return Xt+1 satisfies the pricing equation for the household in country i:
Define ci,t+1 = log (Ci,t+1/Ci,t), xt+1 = log Xi,t+1,
Substituting into (29) gives
For the foreign bond,
Substituting in for this then gives equation (23)
Likewise for the domestic Euler equation, we recover equation (22):
We are grateful for helpful comments from Adrian Peralta Alva, Thorsten Drautzburg, Burcu Eyigungor, Lars Hansen, Daniel Garcia Macia, Divya Kirti, Adrien Verdelhan, Mark Wright, and participants of the Chicago Economic Dynamics working group, the Midwest Macro Conference, the University of Florida economics seminar, the Royal Economic Society Conference, the Federal Reserve Bank of Philadelphia, and the Southern Economic Association Conference.
i.e. when a country’s currency depreciates by 1%, the value of its balance sheet loses 0.32% of GDP, ceteris paribus.
In examining home bias in bonds, we join a large recent literature researching exchange rate exposure and valuation effects on international portfolios, including Cavallo and Tille (2006), Tille (2008), Benigno (2009), Lee, Ghironi, and Rebucci (2009), Matsumoto and Engel (2009), Mendoza, Quadrini, and RiosRull (2009), Lane and Shambaugh (2010b), Corsetti, Dedola, and Leduc (2014), and Maggiori, Neiman, and Schreger (2017) among many others. Gourinchas and Rey (2014) provide a summary of the literature on valuation effects.
To the best of our knowledge, ours is the first paper which features endogenous portfolio decisions and achieves a realistic consumption-real exchange rate correlation. Coeurdacier and Rey (2013) note that most models with endogenous portfolios recover perfect risk-sharing, and that in papers where asset markets are incomplete, consumption and real exchange rates typically remain correlated, as in Benigno and Kucuk-Tuger (2008) and Coeurdacier, Kollmann, and Martin (2010).
After updating the Lane and Shambaugh (2010a) data, Benetrix, Lane, and Shambaugh (2015) show that aggregate exchange rate exposures reversed after 2004 when also accounting for changes to the composition of equity and FDI. However, the debt exposure remains negative – or equivalently, bond home bias remains positive (Figure 1). We consider the debt exposure to be the relevant measure to our analysis, which concerns nominal bonds. While an unbalanced equity portfolio might have risk that is correlated with nominal exchange rates, equities are predominantly real assets, and so that risk is an equilibrium outcome rather than written into the security. Expanding our analysis to equities and other real assets will be a component of future research.
Developed economies follow the definition of Benetrix, Lane, and Shambaugh (2015), namely: Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Israel, Ireland, Italy, Japan, Netherlands, New Zealand, Norway, Portugal, Spain, Sweden, Switzerland, the United Kingdom, and the United States.
Home bias in bond holdings is a also component of the broader home bias in assets, which is puzzling in standard international RBC models; see Lewis (1999) for an early summary, and Coeurdacier and Rey (2013) for a more recent one. When asset returns are uncorrelated with labor income, as in Lucas Jr. (1982), households fully diversify. When domestic asset returns are positively correlated with labor income, households bias their portfolios towards foreign assets, as in Baxter and Jermann (1997). In our model, domestic bond returns are negatively correlated with labor income, so households bias their portfolios towards domestic bonds.
Stationarity holds because on average, interest rates are less than the discount rate.
This algorithm joins the large literature using projection methods to solve macroeconomic models, which Fernndez-Villaverde, Rubio-Ramrez, and Schorfheide (2016) survey.
The Devereux-Sutherland algorithm is presented in Devereux and Sutherland (2011), was developed independently and concurrently by Tille and van Wincoop (2010), and is closely related to the method of Evans and Hnatkovska (2012). Papers that use Devereux-Sutherland to solve endogenous portfolio problems with nominal bonds include Rahbari (2009), Berriel and Bhattarai (2013), Coeurdacier and Gourinchas (2016)
“Currency” here serves the role only of a unit of account, not a means of exchange nor a store of value. Given that we are most interested in wealth effects induced by relative fluctuations in competing units of account, this is an appropriate simplification for our purposes.
Indeed, in the calibrated solution of Section 3, we allow for a richer shock structure, with within-country correlation of the real and nominal shock, both contemporaneously and through the lag structure.
Consistent with our critique of linearization solutions, this argument is not dependent on finding a steady state. It is an approximation around the conditional expectation in the next period give the current state.
Looking ahead to the solution techniques we discuss later, we note that equation (26) is precisely that used by Devereux and Sutherland (2011) to generate linearized solutions to the portfolio problem.
This holds even for methods which produce accurate levels of asset holdings, such as Tille and van Wincoop (2010) and Devereux and Sutherland (2011), because they too rely on linearizing near the steady state interest rate.
Our model is estimated as if two copies of the United States traded with one another. We select this symmetric case for three reasons. First, we choose not to estimate a pair of similar economies (e.g. the US and the Euro-zone) because we want to match the aggregate trade shares, and no two large economies have bilateral flows that are nearly as large as their total trade flows. Second, we choose not to estimate the US versus the rest of the world, because tradable/nontradable shares and prices are not available for the world as a whole. Finally, in this stylized model, we want to be clear that our results are generated by the few economic ingredients, rather than an asymmetry across countries.
We follow Stockman and Tesar (1995) and define tradable sectors as: agriculture, mining, manufacturing, and transportation.
This interpolation is, of course, not unique. But it is if we insist that the quarterly autocorrelations of produtivity and prices are, like their annual counterparts, positive.
This is the same effect as studied in Benigno and Thoenissen (2008), and similar to Corsetti, Dedola, and Leduc (2008), who instead suppose that home and foreign goods are complements. Mukhin, Itskhoki, and others (2016) criticize these mechanisms as being inconsistent with the Meese-Rogoff puzzle and the purchasing power parity puzzle. This criticism at least partially applies to our model; nominal exchange rates are not a random walk, and less correlated with real exchange rates than in the data (Table 5). Engel (1999) also criticizes this channel, finding that tradable prices account for most of the changes in relative price levels at short horizons. Alternative mechanisms through which productivity shocks can produce consumption growth and a real exchange rate decline for some asset market structures include nonseparable utility with news shocks (Colacito and Croce, 2013), nonseparable utility with labor wedge shocks (Karabarbounis, 2014), and financial shocks (Mukhin, Itskhoki, and others, 2016).
We calculate correlations of log quantities for the United States at a quarterly frequency. Income and consumption are taken from the national accounts. Real and nominal exchange rates use the BIS narrow effective exchange rate, which we seasonally adjusted at the quarterly frequency. When reporting correlations of levels, we first remove a linear time trend. Finally, the levels and growth rates are absolute, versus relative to the other country, which is why the consumption-real exchange rate correlation differs from that reported in Table 4.
Hence the average home bias figure in Table 4. Average home assets plus average foreign borrowing gives a GDP-hom bias ratio of 0.78.
A related issue is that of perfect substitutability of assets at the steady state. But this is a solved problem - Devereux and Sutherland (2011) show how to compute the correct approximation to asset holdings in such a model - and distinct from the one we address here. However, that technique also relies on approximating near a steady state interest rate of
This is also the only one of Schmitt-Grohe and Uribe‘s modifications that doesn’t alter the exact mechanism that we are trying to investigate: their ad hoc debt elastic demand curve is an endogenous feature of our model; portfolio adjustment costs would alter the portfolio decision that we want to study; and complete markets are precisely the paradigm that we know fails to produce empirically plausible Backus-Smith correlations.
When we solve the model using a local linearization, we make sure to approximate around the true asset level using the approach of (Devereux and Sutherland, 2011).
There is no commonly accepted strategy for this calibration. Different papers choose values in a wide range, on the order of 10−4 (Rabitsch, Stepanchuk, and Tsyrennikov, 2015) to 10−3 (Devereux and Yetman, 2010) to 10−2 Yao (2012).
There is one alternative method to our gloabl approach, suggested by Devereux and Sutherland (2010): guess a mean interest rate, linearize nearby, simulate, update the interest rate guess, and iterate to convergence. As noted by Rabitsch, Stepanchuk, and Tsyrennikov (2015), this will fail because the analytic solution for average asset holdings computed by local linearization formulae of Devereux and Sutherland (2011) do not hold away from the riskless interest rate.
The basis functions we use for this are the full set of quadratic functions of the states, although this choice is a matter of accuracy rather than anything more fundamental. There are six states in the model: real and nominal shocks in each country, plus stocks of each asset. This means that for each model variable, we solve for coefficients defining the projection onto the intercept, linear, and quadratic iterations for each state, i.e. 1 + 6 + .5 × 6 × 7 = 28 coefficients. With 13 model variables for each country, plus real and nominal exchange rates, this results in some (2 + 2 × 13) × 28 = 784 projection coefficients in total.
Because equilibrium assets holdings and endowments are highly correlated, the conditional distributions of
Each is labeled with a variable name, because the (Maliar and Maliar, 2015) method associates each equation with a rules for one variable. Here, the Euler equations are satisfied by adjusting the rules for
Macroeconomic papers estimate this parameter in a broad range: Taylor (1993) estimates .4, Heathcote and Perri (2002) estimate .9, Whalley (1985) estimates 1.5, and Corsetti, Dedola, and Leduc (2008) estimate 3.3.
A long literature following Bilson (1981) and Fama (1984) tests UIP and typically finds that the correlation is zero or negative. Engel (1996) surveys this evidence and many papers such as Burnside, Eichenbaum, Kleshchelski, and Rebelo (2011) and Menkhoff, Sarno, Schmeling, and Schrimpf (2012) demonstrates that the puzzle still holds in recent data.
The same notation can be easily extended to vector-valued functions y(X,Y) and c(X,Y) by stacking the coefficients into the vectors δy and δc.
Regularized polynomials often have superior performance for approximations of order three and higher. This is because near zero, xn looks very similar for n ≥ 2. As we approximate only to second order, though, we use “raw” unsclaed polynomials.