The Ties that Bind: Measuring International Bond Spillovers Using Inflation-Indexed Bond Yields

Tamim Bayoumi; Andrew J Swiston

doi:10.5089/9781589069121.024.A004

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The Ties that Bind: Measuring International Bond Spillovers Using Inflation-Indexed Bond Yields

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Mr. Tamim Bayoumi

Mr. Tamim Bayoumi
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Mr. Andrew J Swiston

Mr. Andrew J Swiston
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Publication Date:: 29 Jun 2010

eISBN:: 9781589069121

Language:: English

Keywords:: SP; FDI inflow; inflation expectation; trade liberalization; liberalization date; remittance shock; Bank credit; Foreign direct investment; Trade liberalization; Inflation; Real interest rates; East Asia; Global; Africa; Middle East; Southeast Asia; Trade balance; ReformsEmerging market business cycles; remittance FluctuationsStructural reform; real rate of interest; inflation-indexed yield; nominal yield; inflation-indexed market data; inflation-indexed securities; Spillovers; Inflation-indexed bonds; Bond yields

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This paper explores international bond spillovers using daily and weekly data on yields on inflation-indexed bonds and associated inflation expectations for the United States, Australia, Canada, France, Sweden, Japan, and the United Kingdom. The analysis starts in 2002, by which point U.S. inflation-indexed markets had matured. Real bond yields are found to be closely linked across countries, with developments in U.S. markets determining around half of real foreign yields and no evidence of spillovers back to the United States. Spillovers in inflation expectations are smaller and the direction of causation is less clear.

Abstract

One of the many implications of rapid financial market globalization is the likelihood of increasing financial spillovers across countries. This is a particularly important possibility for government bonds, where the standardized characteristics of underlying instruments and rising internationalization of holdings are creating an increasingly interlinked and global market. Yields on government bonds provide the “risk free” interest rate that is the basis for returns in a wide swathe of other markets. Given that yields on long-term securities are generally considered to have a larger impact on activity than the short-term rates that monetary authorities target, globalized markets in government securities provide an important economic as well as financial link between countries.

In the past, one limitation in analyzing these links has been that it is difficult to separate real bond yields, which would be expected to be highly linked across countries, from changes in long-term inflation expectations, which would be heavily influenced by domestic monetary policy. Fortunately, the decomposition of nominal yields into these two components has been greatly assisted by the development of inflation-indexed bonds, which their movements to be continuously tracked. Although indexed bonds were already trading in a number of markets from the early 1990s, it is only with the introduction of inflation-indexed bonds in the United States—the world’s largest and most sophisticated bond market—in January 1997 that the potential to identify international spillovers in real interest rates and inflation expectations could be fully realized. With the U.S. inflation-indexed bond market now over a decade old, there is sufficient information to allow statistical analysis of spillovers in bond yields and inflation expectations.¹

Accordingly, this paper uses government bonds to examine international spillovers between real interest rates and inflation expectations. It analyzes spillovers between the United States and six other industrial countries with inflation-indexed bond markets—Australia, Canada, France, Japan, Sweden, and the United Kingdom. Given the convergence of euro area bond yields since European Monetary Union, the French data (where inflation-indexed bonds were introduced in November 1998) can be taken as a proxy for the euro area as a whole. (Italian data, available since early 2004, are almost identical to the French series.) As a result, the sample covers bond yields in the vast majority of the industrial world, although in the case of Japan inflation-indexed bonds were only issued starting in 2004.

The focus of this paper is on bilateral links between the U.S. markets and other countries. This reflects the dominant position of the United States in the global bond market. Almost two-thirds of all private bonds are traded in U.S. markets, a significantly more important position than in the real economy, where U.S. GDP represents about one-third of the world using market exchange rates and 20 percent using purchasing parity rates. Financial markets are thus a potentially extremely important conduit for spillovers from the United States to the rest of the world.

Indeed, while this is the first paper we know of to examine international spillovers using inflation-indexed bonds, there is a large literature showing that U.S. macroeconomic news affects returns in foreign markets. Faust and others (2007) is a representative example. Using intraday data, they find that when U.S. economic activity turns out stronger than expected or there is a surprise monetary tightening, the dollar appreciates and interest rates in the United Kingdom and the euro area increase. Other works confirming this evidence on exchange rates include Almeida, Goodhart, and Payne (1998); Kim and Sheen (2000); Christie-David, Chaudhry, and Khan (2002); Fair (2003); Andersen and others (2003, 2007); and Ehrmann and Fratzscher (2003, 2005); Goldberg and Leonard (2003) and reach the same conclusions on interest rates. Andersen and others (2007) show how the impact on foreign equity markets varies depending on the state of the economy. Stronger-than-expected U.S. activity raises foreign stock prices during recessions but lowers them during expansions, when concerns about future monetary tightening appear to predominate.

Although U.S. economic releases move foreign markets, there are fewer spillovers in the opposite direction. The response of the German mark or euro-dollar exchange rate is rarely moved by German releases (Anderson and others, 2003 and Almeida, Goodhart, and Payne, 1998), and German and euro area data releases have little impact on U.S. bond yields (Goldberg and Leonard, 2003; Ehrmann and Fratzscher, 2005). In Becker, Finnerty, and Friedman (1995), U.S. news affects the U.K. equity market but U.K. news has no impact on the S&P 500.

The literature on linkages across financial markets also points to the dominance of U.S. spillovers to foreign markets, even when controlling for the role of macroeconomic news. U.S. interest rates drive interest rates in the euro area (Ehrmann and Fratzscher, 2005), Germany (Bremnes, Gjerde, and Soettem, 2001), Canada (Gravelle and Moessner, 2001), and Australia (Kim and Sheen, 2000). Fatum and Scholnick (2006) show that increased expectations of U.S. monetary tightening, as measured by rates on federal funds futures contracts, are associated with an appreciation in the dollar. And there is a higher degree of dependence of foreign equity markets on U.S. markets than vice versa (Becker, Finnerty, and Gupta, 1990; Lin, Engle, and Ito, 1994; and Diebold and Yilmaz, forthcoming). In a framework analyzing U.S.-euro area linkages across short-term interest rates, long-term bond yields, and equity markets, Ehrmann, Fratzscher, and Rigobon (2007) find that the share of variance in euro area markets explained by U.S. markets is, on average, three times as large as the euro area’s importance for U.S. markets.

There is also an active body of work on the interdependence of global real interest rates and their convergence over time, but none using inflation-indexed securities, due to the short period for which data exist. The extant literature typically uses ex post real rates based on inflation outturns, or derives real rates using proxies for inflation expectations. Overall, the evidence for real interest parity is mixed, while studies that examine the response of interest rates by country find some role for U.S. real rates in determining those of other countries.² For example, Chinn and Frankel (2005) find that European rates move so as to restore real interest parity while U.S. rates do not, although there are preliminary indications that this is changing with the advent of the euro area. Cumby and Mishkin (1986) show that European rates respond to movements in U.S. rates, but reject real interest parity because the pass-through is not one-to-one. Breedon, Henry, and Williams (1999) find some evidence that U.S. rates are weakly exogenous for other G7 countries, but cannot reject the same hypothesis for Canada or France. In Chinn and Frankel (1995), U.S. and Japanese real rates have similar influences on emerging Asian markets, but there are no links between the U.S. and Japan or Canada. Thus, the use of more reliable data on real interest rates may clarify the nature of cross-country linkages.

I. The Theory and Practice of Bond Yields

Some Theory

For an investor, the annualized yield on a nominal bond can be divided into a “real” return and a component that reflects expected inflation, both of which can be further divided into an expected value and a risk premium associated with investor preferences. Formally:

\begin{matrix} Y i e l d_{t} = E_{t} (r_{t, t + k} + π_{t, t + k}) + R P_{t} (r_{t, t + k} + π_{t, t + k}), & (1) \end{matrix}

where E is the expectations operator, RP is the risk premium, and r_t,t+k and π_t,t+k are the annualized real rate of interest and of inflation between t and t + k, respectively. By ensuring that the principal of the bond grows with future inflation, the yield on an inflation-indexed bond eliminates the second and fourth terms. Assuming the risk premium is separable, this implies:

\begin{matrix} Y i e l d_{-} I I_{t} & = E_{t} (r_{t, t + k}) + R P_{t} (r_{t, t + k}) a n d Y i e l d_{t} - Y i e l d_{-} I I_{t} \\ = E_{t} (π_{t, t + k}) + R P_{t} (π_{t, t + k}) . & (2) \end{matrix}

Hence, an inflation-indexed bond allows one to differentiate the real rate of interest and associated risk premium from the equivalent information for inflation expectations. The real rate of interest is simply the quoted yield on the inflation-indexed bond, while the difference between the yields of a nominal and inflation-indexed bond of the same maturity is a measure of expectations of average inflation over that horizon.³

For a foreign investor the same equations hold, except that there is also foreign exchange risk because the investor is assumed to be concerned about returns in local currency. Using an asterisk to denote foreign variables gives:

\begin{matrix} Y i e l d_{t}^{*} = E_{t} (r_{t, t + k}^{*} + π_{t, t + k}^{*} + s_{t, t + k}) + R P_{t} (r_{t, t + k} + π_{t, t + k} + s_{t, t + k}) \\ Y i e l d_{-} I I_{t}^{*} = E_{t} (r_{t, t + k}^{*} + r s_{t, t + k}) + R P_{t} (r_{t, t + k}^{*} + r s_{t, t + k}), & (3) \end{matrix}

where s_t,t+k is the annualized nominal appreciation in the bilateral exchange rate and rs_t,t+k is its real equivalent.

Assuming the marginal investor equates real returns across countries, so that $E_{t} (r_{t, t + k}) = E_{t} (r_{t, t + k}^{*} + r s_{t, t + k})$ , it follows that international differences in nominal yields reflect expected future values of inflation and the exchange rate as well as risk premiums on real rates, inflation, and exchange rates. Those on index-linked bonds isolate the risk premium on real interest rates and exchange rates while cross-country differentials in the gap between yields on nominal and inflation-indexed bonds reflect expectations and risk premiums associated with the future path of inflation:

\begin{matrix} Y i e l d_{t} - Y i e l d_{t}^{*} = E_{t} (π_{t, t + k} - π_{t, t + k}^{*} - r s_{t, t + k}) + R P_{t} (r_{t, t + k} - r_{t, t + k}^{*} + π_{t, t + k} - π_{t, t + k}^{*} - r s_{t, t + k}) \\ Y i e l d_{-} I I_{t} - Y i e l d_{-} I I_{t}^{*} = R P_{t} (r_{t, t + k} - r_{t, t + k}^{*} - r s_{t, t + k}) \\ (Y i e l d_{t} - Y i e l d_{-} I I_{t}) - (Y i e l d_{t}^{*} - Y i e l d_{-} I I_{t}^{*}) = E_{t} (π_{t, t + k} - π_{t, t + k}^{*}) + R P_{t} (π_{t, t + k} - π_{t, t + k}^{*}) & (4) \end{matrix}

In short, international comparisons of inflation-indexed yields and the differences between conventional and inflation-indexed yields should separate real risk premiums from expected inflation differentials and their associated risk premiums.

The Data

We collected daily data on closing prices of both conventional and inflation-indexed bonds for advanced economies that have issued inflation-linked government securities: the United States, Australia, Canada, France, Italy, Japan, Sweden, and the United Kingdom. Most of our data start in 1997, when the United States issued its first inflation-indexed security, and finishes at end-2006. By the start of 1997, the Australian, Canadian, Swedish, and U.K. markets had already been trading for some time, although due to data limitations in the case of Sweden our series only starts in June 2000.⁴ The French inflation-indexed market data are only available from November 1998, when the market opened, but in the case of Italy and Japan the markets opened in 2004.

Given the short sample available for the Italian data, we only use it to confirm that the French markets are a good approximation for the euro area as a whole (the correlation coefficient across daily changes in the French and Italian real interest rate series is 0.98).⁵ Japanese results are reported, however, as the zero interest rate policy being followed through July 2006 means that these results provide potential insights into the impact of this unique policy on the country’s linkages with other financial markets. The earlier working paper version of this study also includes tests using intraday conventional bonds for a relatively short window (Bayoumi and Swiston, 2007).

Figure 1 graphs end-week nominal government bond yields, real yields, and implied inflation expectations for the full sample except Italy and Japan since the start of 1997. Weekly closes are plotted to increase the clarity of the lines. For the United States the series correspond to the government’s benchmark 10-year maturity, but for the other countries the inflation-indexed yield is on the bond maturing closest to 10 years and typically ranges from eight to 12 years.⁶ The nominal yield for those countries is from a bond whose maturity is as close as possible to the indexed bond, which allows for the calculation of expected inflation over that horizon.

Figure 1.

Long-term Interest Rates and Inflation Expectations

Citation: IMF Staff Papers 2010, 002; 10.5089/9781589069121.024.A004

Sources: Bloomberg, L.P.; and authors’ calculations.Note: Yields on inflation-indexed securities are as close as possible to the 10-year maturity. Yields on nominal securities are selected to match the maturity date of each country’s corresponding inflation-indexed security. Inflation expectations are calculated as the difference between the nominal and inflation-indexed yield.

The first feature to note in the upper panel of Figure 1 is the high correlation of nominal bond yields across countries. Both the trends and higher-frequency wobbles appear highly correlated across countries. Looking at the start of the sample, for example, nominal yields in all countries in the sample fell steadily from early 1997 through mid- to late 1998 and then rose again through early 2000. Yields then trended downward through 2003 and have generally remained at very low levels. On the other hand, there is some variation. For example, Australia has tended to have higher yields than other countries, but more recently France and Sweden have had the lowest yields. In addition, U.S. yields seem to have been particularly low in 2002 and early 2003, possibly reflecting the aggressive reductions in short-term policy rates at that time.

The middle panel shows real yields (that is, those on inflation-indexed bonds), using the same size for the vertical scale (6 percentage points) to aid comparison. In addition to being somewhat smoother than their nominal counterparts, their movements are less correlated across countries. For example, while real yields fell significantly through the sample for all countries, this reduction occurred much earlier in the United Kingdom than elsewhere. By contrast, inflation expectations (that is, the differential between conventional and index-linked bonds), shown in the lower panel of the figure, have shown little evidence of a trend over the sample.

Figure 2 shows the same data since the start of 2004 with Italy and Japan added. The Italian data are virtually identical to the French series, confirming that France is a reasonable proxy for the euro area. Movements in Japanese yields and inflation expectations are less correlated with the other countries, a result of particular interest given that country’s unique zero short-term interest rate policy to combat deflation.

Figure 2.

Long-term Interest Rates and Inflation Expectations

Citation: IMF Staff Papers 2010, 002; 10.5089/9781589069121.024.A004

Table 1, which reports standard deviations of daily closes for these markets, confirms some of these observations. For instance, the standard deviations of the level of real returns are similar to those for nominal yields, but changes in nominal rates are more volatile than either real rates or inflation expectations. The standard deviations of the level of inflation expectations are lower than for either nominal or real yields, an indication of the long-term credibility of the monetary authorities in these countries. As in the remainder of this paper, the calculations use data starting in 2002, as it is only from this period that the U.S. inflation-indexed markets were liquid enough for yields to accurately reflect market perceptions of real interest rates and inflation expectations (Sack and Elsasser, 2004; and Shen, 2006).⁷

Table 1.

Standard Deviations of Daily Bond Yields and Inflation Expectations

(January 2, 2002 to December 29, 2006)

Source: Authors’ calculations. Note: See note to Figure 1. Data for Japan begin in April 2004. Standard deviations are calculated on the daily change in yields, in basis points.

Table 1.

Standard Deviations of Daily Bond Yields and Inflation Expectations

(January 2, 2002 to December 29, 2006)

	Nominal Yields		Real Yields		Inflation Expectations
	Level	Changes	Level	Changes	Level	Changes
Australia	0.35	0.06	0.45	0.03	0.39	0.04
Canada	0.57	0.04	0.72	0.02	0.25	0.03
France	0.71	0.04	0.75	0.03	0.17	0.02
Japan	0.21	0.03	0.23	0.03	0.16	0.02
Sweden	0.81	0.04	0.70	0.03	0.20	0.03
United Kingdom	0.33	0.04	0.33	0.03	0.23	0.02
United States	0.44	0.06	0.47	0.04	0.35	0.03

Source: Authors’ calculations. Note: See note to Figure 1. Data for Japan begin in April 2004. Standard deviations are calculated on the daily change in yields, in basis points.

Table 1.

Standard Deviations of Daily Bond Yields and Inflation Expectations

(January 2, 2002 to December 29, 2006)

	Nominal Yields		Real Yields		Inflation Expectations
	Level	Changes	Level	Changes	Level	Changes
Australia	0.35	0.06	0.45	0.03	0.39	0.04
Canada	0.57	0.04	0.72	0.02	0.25	0.03
France	0.71	0.04	0.75	0.03	0.17	0.02
Japan	0.21	0.03	0.23	0.03	0.16	0.02
Sweden	0.81	0.04	0.70	0.03	0.20	0.03
United Kingdom	0.33	0.04	0.33	0.03	0.23	0.02
United States	0.44	0.06	0.47	0.04	0.35	0.03

Source: Authors’ calculations. Note: See note to Figure 1. Data for Japan begin in April 2004. Standard deviations are calculated on the daily change in yields, in basis points.

Table 2 reports correlations of nominal yields, real yields, and inflation expectations, with correlations of changes reported in the lower left triangle and levels in the upper right one. Levels of nominal yields are relatively highly correlated: most entries are above ½ with the slightly surprising exception of some of the entries involving the United States, where the low correlations appear to reflect the specific sample used.⁸ Correlations of daily changes in nominal yields are generally lower than their counterparts in levels, and partly reflect regional linkages (including greater overlap of trading times, as discussed further below). Correlations are high between the three European markets (France, Sweden, and the United Kingdom), between the two North American markets (Canada and the United States), and, to a less extent, across these two sets of markets.

Table 2.

Cross-Country Correlations in Bond Yields and Inflation Expectations

(January 2, 2002 to December 29, 2006)

Source: Authors’ calculations. Note: See note to Figure 1. Data for Japan begin in April 2004. Entries above the diagonal are correlations of the data in levels; entries below the diagonal are correlations of daily changes.

Table 2.

Cross-Country Correlations in Bond Yields and Inflation Expectations

(January 2, 2002 to December 29, 2006)

		Australia	Canada	France	Japan	Sweden	United Kingdom	United States
Nominal Yields			Levels
Australia		−	0.59	0.77	0.75	0.66	0.89	0.72
Canada	Changes	0.12	−	0.94	0.49	0.97	0.59	0.06
France		0.27	0.58	−	0.73	0.97	0.73	0.29
Japan		0.40	0.13	0.22	−	0.60	0.59	0.71
Sweden		0.37	0.44	0.83	0.27	−	0.67	0.09
United Kingdom		0.26	0.51	0.88	0.22	0.76	−	0.56
United States		0.06	0.84	0.58	0.13	0.42	0.51	−
Real Yields			Levels
Australia		−	0.89	0.80	0.26	0.90	0.86	0.36
Canada	Changes	0.14	−	0.93	0.23	0.97	0.85	0.52
France		0.19	0.46	−	0.67	0.97	0.90	0.77
Japan		0.33	0.12	0.17	−	0.43	0.21	0.69
Sweden		0.27	0.30	0.54	0.26	−	0.90	0.62
United Kingdom		0.18	0.39	0.71	0.18	0.48	−	0.61
United States		0.08	0.54	0.49	0.12	0.27	0.40	−
Inflation Expectations			Levels
Australia		−	0.58	0.29	0.00	−0.14	0.66	0.58
Canada	Changes	0.04	−	0.68	0.48	0.06	0.69	0.86
France		0.13	0.32	−	0.25	0.47	0.81	0.77
Japan		0.08	0.05	0.05	−	0.15	0.00	0.39
Sweden		0.24	0.30	0.49	0.05	−	0.27	−0.06
United Kingdom		0.14	0.31	0.44	0.02	0.37	−	0.81
United States		−0.07	0.51	0.26	0.05	0.20	0.21	−

Table 2.

Cross-Country Correlations in Bond Yields and Inflation Expectations

(January 2, 2002 to December 29, 2006)

		Australia	Canada	France	Japan	Sweden	United Kingdom	United States
Nominal Yields			Levels
Australia		−	0.59	0.77	0.75	0.66	0.89	0.72
Canada	Changes	0.12	−	0.94	0.49	0.97	0.59	0.06
France		0.27	0.58	−	0.73	0.97	0.73	0.29
Japan		0.40	0.13	0.22	−	0.60	0.59	0.71
Sweden		0.37	0.44	0.83	0.27	−	0.67	0.09
United Kingdom		0.26	0.51	0.88	0.22	0.76	−	0.56
United States		0.06	0.84	0.58	0.13	0.42	0.51	−
Real Yields			Levels
Australia		−	0.89	0.80	0.26	0.90	0.86	0.36
Canada	Changes	0.14	−	0.93	0.23	0.97	0.85	0.52
France		0.19	0.46	−	0.67	0.97	0.90	0.77
Japan		0.33	0.12	0.17	−	0.43	0.21	0.69
Sweden		0.27	0.30	0.54	0.26	−	0.90	0.62
United Kingdom		0.18	0.39	0.71	0.18	0.48	−	0.61
United States		0.08	0.54	0.49	0.12	0.27	0.40	−
Inflation Expectations			Levels
Australia		−	0.58	0.29	0.00	−0.14	0.66	0.58
Canada	Changes	0.04	−	0.68	0.48	0.06	0.69	0.86
France		0.13	0.32	−	0.25	0.47	0.81	0.77
Japan		0.08	0.05	0.05	−	0.15	0.00	0.39
Sweden		0.24	0.30	0.49	0.05	−	0.27	−0.06
United Kingdom		0.14	0.31	0.44	0.02	0.37	−	0.81
United States		−0.07	0.51	0.26	0.05	0.20	0.21	−

Switching to the constituent parts of nominal rates, real rates appear more correlated than inflation expectations in both levels and changes. Correlations of levels of real rates all exceed 0.8 with the exception of those for Japan and, again somewhat surprisingly, the United States (where this result again appears to reflect the specific sample). By contrast, correlations of levels of inflation expectations are almost universally much lower, varying between −0.14 and 0.86. The data on changes in real rates and inflation expectations again show the regional patterns observed for nominal rates. Despite high correlations in levels, formal tests (not shown here for brevity) reject cointegration between the United States and other countries for all three series, although given the short sample (only four years) these results are not conclusive.

How do these observations accord with the theory outlined earlier? The high correlations across real rates are consistent with the notion that there are significant trends in “world” real rates, and hence the possibility for significant spillovers. The lower correlations among inflation expectations can be explained by the idea that inflation is more heavily influenced by domestic factors than global factors.

II. Tests for Efficiency and the Existence of Spillovers

This section establishes definitions of market efficiency and spillovers, and carries out tests to distinguish which of the two exist in international bond markets. A financial market is efficient if market prices fully reflect available information.⁹ Market efficiency implies that the current period rate of return on a security is the best forecast of the future rate of return:

\begin{matrix} E_{t} (r_{i, t + 1} | Φ_{t}) = r_{i, t}, & (5) \end{matrix}

or, subtracting r_i,t from both sides:

\begin{matrix} E_{t} (r_{i, t + 1} - r_{i, t} | Φ_{t}) = 0, & (6) \end{matrix}

where r_i,t is the return on asset i at time t and Φ represents the set of available information.¹⁰ If the above equations did not hold, for example if the expected return in t + 1 exceeded the return in t, then the price of the security should be bid up in t. No information available at t should systematically predict the asset’s return in t + 1. We test a weak form of this efficiency, in which the only information incorporated in our efficiency tests is of an asset’s own historical returns and those of related markets.

Ideally, a test of spillovers would include not only the impact of prior information from foreign markets, but be able to distinguish the extent to which any contemporaneous correlation between the two markets is the result of developments in the foreign market:

\begin{matrix} r_{t} = f (r_{t}^{*}, r_{t - 1}^{*}) . & (7) \end{matrix}

If $r_{t}^{*}$ is a significant determinant of r_t, then there are spillovers from the foreign to the domestic market, while if it can be determined that $r_{t - 1}^{*}$ matters for r_t, then there is evidence both of spillovers and of domestic market inefficiencies. The difficulty in assigning the contemporaneous correlation between r_t and $r_{t}^{*}$ to developments in one market or the other is well known, so this section uses various tests of the impact of $r_{t - 1}^{*}$ on r_t to reach conclusions regarding the most likely driver of the correlation between the two markets.

A complication with this analysis is that international bond markets are open at different times of the day, and hence the definition of prior information can be somewhat tricky (Figure 3). The main trading session for U.S. bonds opens at 7 am eastern standard time (EST) and the fix in the data is generally 4.30 pm.¹¹ The other countries fall into three categories:

Figure 3.

Intraday Price Quote Times

Citation: IMF Staff Papers 2010, 002; 10.5089/9781589069121.024.A004

Source: Bloomberg, L.P.Note: The figure shows times according to Eastern Standard Time in the United States. The bar for the United States shows hours for the main trading session; price quotes are nearly continuous from 6:30 pm Sunday to 5:00 pm Friday.

Asian markets (no overlap). The Australian (4.30 pm to 12.30 am EST) and Japanese (7 pm to 5 am EST) markets have no overlap with the main U.S. trading hours.
European markets (significant overlap). The French, Swedish, and U.K. markets open before the U.S. market (at 1.30 am EST for France and Sweden, 2.30 am for the United Kingdom) and the closing quote is for 1.30 pm EST, about two-thirds of the way through the U.S. session. To add a further complication, the U.S. market is most active during the overlap with the European markets.
Canadian market (synchronous). The Canadian market has essentially the same trading hours as in the United States.

Market Efficiency Tests Using Daily Data

As discussed above, the daily data comprise changes in yields from the fix on one day to the fix the next day, which means that longer lags are needed on the foreign variables to ensure no overlap of trading times. In particular, as the U.S. market closes later than other markets (except Canada), it is necessary to lag the change in U.S. yields two days vs. one day for the foreign markets to ensure no overlap in trading times.

This is an eminently sensible approach for Australia and Japan, where local trading closes before U.S. markets open (in the case of Canadian markets, where the trading sessions cover the same time period, the first lag of U.S. yields can be used). However, for the European markets—where there is a large overlap of the trading sessions—it results in using relatively outdated U.S. information. To see this, consider the test of the degree to which U.S. and U.K. markets interact. In the regression testing the influence of changes in U.S. yields on their U.K. counterparts, the lagged U.S. data are 21 hours “older” than the lagged U.K. yields, whereas in the reverse case the difference is only three hours. Thus, the results presented here put U.S. markets at a disadvantage in establishing the existence of spillovers.

The tests use the following specification:

\begin{array}{l} I n d e x - l i n k e d b o n d s a n d a s s o c i a t e d I n f l a t i o n E x p e c t i o n s \\ \begin{matrix} Δ r_{t} o r Δ p_{t} = & α + β_{1} Δ r_{t - 1} + β_{2} r_{t - 1} + β_{3} Δ p_{t - 1} + β_{4} p_{t - 1} \\ + γ_{1} Δ r_{t - 1}^{*} + + γ_{2} r_{t - 1}^{*} + + γ_{3} Δ p_{t - 1}^{*} + + γ_{4} p_{t - 1}^{*} + ε_{t} \\ Δ r_{t}^{*} o r Δ p_{t}^{*} = & α + β_{1} Δ r_{t - 1}^{*} + β_{2} r_{t - 1}^{*} + β_{3} Δ p_{t - 1}^{*} + β_{4} p_{t - 1}^{*} \\ + γ_{1} Δ r_{t - 1} + + γ_{2} r_{t - 1} + + γ_{3} Δ p_{t - 1} + + γ_{4} p_{t - 1} + ε_{t} & (8) \end{matrix} \end{array}

\begin{matrix} C o n v e n t i o n a l B o n d s \\ Δ i_{t} = α + β_{1} Δ i_{t - 1} + β_{2} i_{t - 1} + γ_{1} Δ i_{t - 1}^{*} + γ_{2} i_{t - 1}^{*} + ε_{t} \\ Δ i_{t}^{*} = α + β_{1} Δ i_{t - 1}^{*} + β_{2} i_{t - 1}^{*} + γ_{1} Δ i_{t - 1} + γ_{2} i_{t - 1} + ε_{t}, & (9) \end{matrix}

where r_t, p_t, and i_t represent the real interest rate, associated inflation expectations, and nominal interest rates and the subscript t–1 is understood to mean prior data, as discussed above. Both systems involve first lags of the level and the difference of all variables in the system, and are thus a reparameterization of a vector autoregression (VAR) using two lags of the levels of r_t, $r_{t}^{*}$ , p_t and $p_{t}^{*}$ , or i_t and $i_{t}^{*}$ . The lag length was determined by examining standard tests for the optimal lag length of such a levels VAR. As the tests almost universally pointed to zero, one, or two lags, the specification above—which, as noted above, is equivalent to a VAR in levels with two lags except for parts of the lag structure—was adopted.

These specifications allow for a wide range of tests of efficiency. They are most easily explained using the specification for conventional bonds. Clearly, if excluding the change or level of the other countries’ yields (setting γ₁ = γ₂ = 0) significantly lowers the regression’s fit, then there is evidence for foreign spillovers. Similarly, a significant loss in the regression’s explanatory power due to the exclusion of past domestic yields (setting β₁ = β₂ = 0) is a sign of domestic market inefficiency.

In addition, by testing the variables individually one can also gain information as to the form of the inefficiency. If the current change in the yield depends on domestic or foreign past levels of yields (the regressions’ fit declines significantly if β₂ or γ₂ is excluded) this is a sign of error correction or mean reversion, a phenomenon we will call “long-run inefficiency.” Long-run inefficiency indicates that future short-run returns are predictable based on the difference of current returns from the long-run equilibrium.¹² On the other hand, dependence of current changes in yields on past changes implies a more transitory dependence, which we will label “short-term inefficiency.”

Results of these tests are presented in Table 3. The table reports the p-values of Wald tests of the regressions’ goodness of fit under the coefficient restrictions described above—whether the change in current yields depends significantly on lagged changes in domestic or foreign yields (short-run inefficiency), levels of these yields (long-run inefficiency), or both (overall inefficiency). The results suggest that:

Table 3.

International Bond Market Spillovers at a Daily Frequency

(p-values: January 2, 2002 to December 29, 2006)

Source: Authors’ calculations. Note: Changes in interest rates and inflation expectations for each country are regressed on past levels and changes in interest rates and inflation expectations for the countries listed below and on past levels and changes in U.S. interest rates and inflation expectations. The regressions in Panel C do not include inflation expectations, p-values for three Wald tests are reported: (1) the exclusion of past changes in the dependent variables (short-run); (2) the exclusion of past levels of the dependent variables (long-run); and (3) the exclusion of both past changes in and past levels of the dependent variables (overall). Low p-values imply that the excluded variables are statistically significant determinants of current changes in interest rates or inflation expectations. Each panel contains four columns reporting, from left to right, results of the following tests: (1) the role of past U.S. variables in foreign markets; (2) the role of past domestic information in foreign markets; (3) the role of past foreign information in the U.S. market; and (4) the role of past domestic information in the U.S. market. Regressions for Japan begin in April 2004. p-values reported in bold are significant at the 5 percent level; those reported in bold italics are significant at the 1 percent level.

Table 3.

International Bond Market Spillovers at a Daily Frequency

(p-values: January 2, 2002 to December 29, 2006)

	Panel A. Real Interest Rates				Panel B. Inflation Expectations				Panel C. Nominal Interest Rates
	Foreign market		U.S. market		Foreign market		U.S. market		Foreign market		U.S. market
	United States	Domestic	Foreign	Domestic	United States	Domestic	Foreign	Domestic	United States	Domestic	Foreign	Domestic
Australia
Short-run	0.06	*0.01*	0.97	0.11	0.03	0.30	*0.01*	*0.00*	0.12	0.04	0.15	0.07
Long-run	0.28	0.08	0.26	0.14	0.44	0.04	0.41	0.17	0.01	0.67	0.21	0.37
Overall	0.12	*0.00*	0.33	0.06	0.05	0.04	0.03	*0.00*	0.08	*0.01*	0.16	0.10
Canada
Short-run	0.50	*0.00*	0.60	0.30	0.13	*0.00*	0.14	*0.00*	0.03	0.10	0.38	0.10
Long-run	*0.00*	*0.00*	0.19	0.18	0.06	0.01	0.06	0.58	0.22	0.24	0.04	0.01
Overall	0.04	*0.00*	0.33	0.25	0.18	*0.00*	0.08	0.02	0.10	0.03	0.06	0.01
France
Short-run	0.96	0.37	0.42	0.21	0.31	0.02	0.16	*0.00*	0.62	0.82	0.10	0.02
Long-run	*0.01*	*0.00*	0.91	0.23	0.65	0.25	*0.00*	*0.00*	0.07	0.83	0.25	0.04
Overall	0.03	*0.00*	0.67	0.21	0.49	0.02	*0.00*	*0.00*	0.95	0.18	0.10	*0.00*
Japan
Short-run	0.99	*0.01*	0.53	0.44	0.14	*0.00*	0.77	0.48	0.97	0.49	0.26	0.14
Long-run	0.12	0.01	0.36	0.51	*0.01*	*0.00*	0.93	0.16	0.03	0.12	0.70	0.30
Overall	0.47	*0.00*	0.51	0.62	0.20	*0.00*	0.89	0.30	0.21	0.06	0.45	0.23
Sweden
Short-run	0.80	*0.00*	0.89	0.30	0.17	*0.01*	0.53	*0.00*	0.61	0.32	0.49	0.06
Long-run	0.01	*0.00*	0.35	0.17	0.84	*0.00*	0.07	*0.01*	0.14	0.73	0.11	0.02
Overall	0.12	*0.00*	0.59	0.22	0.39	*0.00*	0.26	*0.00*	0.58	0.36	0.20	*0.01*
United Kingdom
Short-run	0.80	0.25	0.06	0.16	0.05	0.07	0.14	*0.00*	0.65	0.62	*0.01*	*0.00*
Long-run	*0.01*	*0.00*	0.22	0.20	0.43	0.02	0.07	*0.01*	0.03	0.88	0.27	0.10
Overall	0.06	*0.00*	0.06	0.13	0.14	0.02	0.08	*0.00*	0.85	0.09	*0.01*	*0.00*

Table 3.

International Bond Market Spillovers at a Daily Frequency

(p-values: January 2, 2002 to December 29, 2006)

	Panel A. Real Interest Rates				Panel B. Inflation Expectations				Panel C. Nominal Interest Rates
	Foreign market		U.S. market		Foreign market		U.S. market		Foreign market		U.S. market
	United States	Domestic	Foreign	Domestic	United States	Domestic	Foreign	Domestic	United States	Domestic	Foreign	Domestic
Australia
Short-run	0.06	*0.01*	0.97	0.11	0.03	0.30	*0.01*	*0.00*	0.12	0.04	0.15	0.07
Long-run	0.28	0.08	0.26	0.14	0.44	0.04	0.41	0.17	0.01	0.67	0.21	0.37
Overall	0.12	*0.00*	0.33	0.06	0.05	0.04	0.03	*0.00*	0.08	*0.01*	0.16	0.10
Canada
Short-run	0.50	*0.00*	0.60	0.30	0.13	*0.00*	0.14	*0.00*	0.03	0.10	0.38	0.10
Long-run	*0.00*	*0.00*	0.19	0.18	0.06	0.01	0.06	0.58	0.22	0.24	0.04	0.01
Overall	0.04	*0.00*	0.33	0.25	0.18	*0.00*	0.08	0.02	0.10	0.03	0.06	0.01
France
Short-run	0.96	0.37	0.42	0.21	0.31	0.02	0.16	*0.00*	0.62	0.82	0.10	0.02
Long-run	*0.01*	*0.00*	0.91	0.23	0.65	0.25	*0.00*	*0.00*	0.07	0.83	0.25	0.04
Overall	0.03	*0.00*	0.67	0.21	0.49	0.02	*0.00*	*0.00*	0.95	0.18	0.10	*0.00*
Japan
Short-run	0.99	*0.01*	0.53	0.44	0.14	*0.00*	0.77	0.48	0.97	0.49	0.26	0.14
Long-run	0.12	0.01	0.36	0.51	*0.01*	*0.00*	0.93	0.16	0.03	0.12	0.70	0.30
Overall	0.47	*0.00*	0.51	0.62	0.20	*0.00*	0.89	0.30	0.21	0.06	0.45	0.23
Sweden
Short-run	0.80	*0.00*	0.89	0.30	0.17	*0.01*	0.53	*0.00*	0.61	0.32	0.49	0.06
Long-run	0.01	*0.00*	0.35	0.17	0.84	*0.00*	0.07	*0.01*	0.14	0.73	0.11	0.02
Overall	0.12	*0.00*	0.59	0.22	0.39	*0.00*	0.26	*0.00*	0.58	0.36	0.20	*0.01*
United Kingdom
Short-run	0.80	0.25	0.06	0.16	0.05	0.07	0.14	*0.00*	0.65	0.62	*0.01*	*0.00*
Long-run	*0.01*	*0.00*	0.22	0.20	0.43	0.02	0.07	*0.01*	0.03	0.88	0.27	0.10
Overall	0.06	*0.00*	0.06	0.13	0.14	0.02	0.08	*0.00*	0.85	0.09	*0.01*	*0.00*

For real interest rates there is strong evidence of spillovers from U.S. markets abroad and no evidence of reverse causation. The tests reveal that past U.S. yields spillover (Granger-cause) current foreign yields in four of the six other countries, the exceptions being Australia (where the test fails only marginally) and Japan (which has a short sample). In addition, consistent with the “old” nature of some of the U.S. lagged data, most of these spillovers reflect “long-run” linkages while in many cases domestic markets fail the “short-term” test of efficiency, suggesting that the more up-to-the-moment domestic data could be capturing some of the spillovers from the United States. By contrast, none of the 36 entries for the United States are significant at conventional levels.
For inflation expectations the evidence for spillovers is weaker and more mixed with regard to market efficiency. U.S. inflation expectations Granger-cause their foreign counterparts in two of six markets. In addition, all of the foreign markets are inefficient with regard to their own past yields. However, these characteristics—domestic inefficiency and some foreign spillovers—also appear prevalent for U.S. expectations, suggesting that domestic factors are more important for inflation expectations than for real interest rates.
For nominal yields there is strong evidence of U.S. spillovers to foreign markets and some signs of a limited reverse effect. There are significant U.S. spillovers in four of six foreign markets, while spillovers in the other direction only occur in two markets. The evidence on domestic inefficiency is more surprising. Although only two foreign markets show signs that past prices help forecast current ones, several tests indicate domestic inefficiency in the highly liquid U.S. market. The types of spillovers present again reflect a range of linkages.

Market Efficiency: Robustness Checks

An important potential criticism of this approach is that the decomposition of nominal yields into real interest rates and inflation expectations can be distorted by time-varying risk premiums across markets. If shifts in risk aversion affect markets for nominal securities more than their index-linked counterparts, then daily changes in real interest rates and derived inflation expectations could reflect movements in investor sentiment rather than economic fundamentals. If this short-term variation in risk tolerance is linked across countries, it could lead to the finding of spillovers where none truly exist. We use a common measure of market volatility, the VIX index, to control for investor risk aversion. The efficiency regressions are augmented with the contemporaneous value and first two lags of the change in the VIX. The results, reported in Table 4, are very similar to those in Table 3. This suggests that global shifts in risk aversion are not driving common movements in interest rates and inflation expectations.

Table 4.

International Bond Market Spillovers Controlling for Risk Aversion

(p-values: January 2, 2002 to December 29, 2006)

Source: Authors’ calculations. Note: Changes in interest rates and inflation expectations for each country are regressed on past levels and changes in interest rates and inflation expectations for the countries listed below and on past levels and changes in U.S. interest rates and inflation expectations. The regressions in Panel C do not include inflation expectations, p-values for three Wald tests are reported: (1) the exclusion of past changes in the dependent variables (short-run); (2) the exclusion of past levels of the dependent variables (long-run); and (3) the exclusion of both past changes in and past levels of the dependent variables (overall). Low p-values imply that the excluded variables are statistically significant determinants of current changes in interest rates or inflation expectations. Each panel contains four columns reporting, from left to right, results of the following tests: (1) the role of past U.S. variables in foreign markets; (2) the role of past domestic information in foreign markets; (3) the role of past foreign information in the U.S. market; and (4) the role of past domestic information in the U.S. market. All regressions contain contemporaneous and lagged changes in the VIX equity market volatility index as a control for risk aversion. Regressions for Japan begin in April, 2004. p-values reported in bold are significant at the 5 percent level; those reported in bold italics are significant at the 1 percent level.

Table 4.

International Bond Market Spillovers Controlling for Risk Aversion

(p-values: January 2, 2002 to December 29, 2006)

	Real Interest Rates				Inflation Expectations				Nominal Interest Rates
	Foreign market		U.S. market		Foreign market		U.S. market		Foreign market		U.S. market
	United States	Domestic	Foreign	Domestic	United States	Domestic	Foreign	Domestic	United States	Domestic	Foreign	Domestic
Australia
Short-run	0.07	0.14	0.67	*0.01*	0.10	0.84	*0.00*	*0.00*	0.65	0.30	0.63	0.17
Long-run	0.13	0.03	0.51	0.78	0.56	0.11	0.18	0.06	*0.00*	0.21	0.18	0.53
Overall	0.15	*0.01*	0.58	0.04	0.06	0.07	*0.01*	*0.00*	0.14	0.02	0.29	0.25
Canada
Short-run	0.47	*0.00*	0.35	0.09	0.15	*0.00*	0.28	*0.00*	0.03	0.07	0.03	0.33
Long-run	*0.00*	*0.00*	0.15	0.75	0.04	*0.01*	0.23	0.18	0.20	0.37	0.26	0.04
Overall	0.05	*0.00*	0.43	0.25	0.14	*0.00*	0.05	*0.00*	0.11	0.03	0.08	0.03
France
Short-run	0.99	0.28	0.30	0.03	0.41	*0.00*	0.02	*0.00*	0.84	0.68	0.06	0.05
Long-run	*0.00*	*0.00*	0.82	0.79	0.93	0.08	*0.01*	*0.00*	0.18	0.74	0.82	0.06
Overall	0.02	*0.00*	0.56	0.11	0.41	0.02	*0.00*	*0.00*	0.93	0.17	0.13	0.01
Japan
Short-run	0.99	*0.01*	0.54	0.37	0.14	*0.00*	0.73	0.38	0.84	0.59	0.23	0.12
Long-run	0.13	0.01	0.38	0.53	*0.01*	*0.00*	0.91	0.15	0.04	0.14	0.74	0.28
Overall	0.49	*0.00*	0.54	0.55	0.20	*0.00*	0.89	0.23	0.24	0.08	0.44	0.20
Sweden
Short-run	0.96	*0.00*	0.96	0.04	0.45	*0.00*	0.75	*0.00*	0.31	0.45	0.58	0.26
Long-run	0.03	0.03	0.12	0.52	0.22	*0.00*	0.07	*0.01*	0.25	0.74	0.32	0.05
Overall	0.14	*0.00*	0.47	0.13	0.29	*0.00*	0.23	*0.00*	0.51	0.43	0.49	0.06
United Kingdom
Short-run	0.64	0.12	0.13	0.02	0.10	0.03	0.03	*0.00*	0.59	0.35	*0.00*	0.02
Long-run	*0.00*	*0.00*	0.32	0.88	0.12	*0.00*	0.17	*0.01*	0.01	0.36	0.34	0.17
Overall	0.07	*0.00*	0.15	0.10	0.10	0.01	0.03	*0.00*	0.70	0.09	*0.01*	0.02

Source: Authors’ calculations. Note: Changes in interest rates and inflation expectations for each country are regressed on past levels and changes in interest rates and inflation expectations for the countries listed below and on past levels and changes in U.S. interest rates and inflation expectations. The regressions in Panel C do not include inflation expectations, p-values for three Wald tests are reported: (1) the exclusion of past changes in the dependent variables (short-run); (2) the exclusion of past levels of the dependent variables (long-run); and (3) the exclusion of both past changes in and past levels of the dependent variables (overall). Low p-values imply that the excluded variables are statistically significant determinants of current changes in interest rates or inflation expectations. Each panel contains four columns reporting, from left to right, results of the following tests: (1) the role of past U.S. variables in foreign markets; (2) the role of past domestic information in foreign markets; (3) the role of past foreign information in the U.S. market; and (4) the role of past domestic information in the U.S. market. All regressions contain contemporaneous and lagged changes in the VIX equity market volatility index as a control for risk aversion. Regressions for Japan begin in April, 2004. p-values reported in bold are significant at the 5 percent level; those reported in bold italics are significant at the 1 percent level.

Table 4.

International Bond Market Spillovers Controlling for Risk Aversion

(p-values: January 2, 2002 to December 29, 2006)

	Real Interest Rates				Inflation Expectations				Nominal Interest Rates
	Foreign market		U.S. market		Foreign market		U.S. market		Foreign market		U.S. market
	United States	Domestic	Foreign	Domestic	United States	Domestic	Foreign	Domestic	United States	Domestic	Foreign	Domestic
Australia
Short-run	0.07	0.14	0.67	*0.01*	0.10	0.84	*0.00*	*0.00*	0.65	0.30	0.63	0.17
Long-run	0.13	0.03	0.51	0.78	0.56	0.11	0.18	0.06	*0.00*	0.21	0.18	0.53
Overall	0.15	*0.01*	0.58	0.04	0.06	0.07	*0.01*	*0.00*	0.14	0.02	0.29	0.25
Canada
Short-run	0.47	*0.00*	0.35	0.09	0.15	*0.00*	0.28	*0.00*	0.03	0.07	0.03	0.33
Long-run	*0.00*	*0.00*	0.15	0.75	0.04	*0.01*	0.23	0.18	0.20	0.37	0.26	0.04
Overall	0.05	*0.00*	0.43	0.25	0.14	*0.00*	0.05	*0.00*	0.11	0.03	0.08	0.03
France
Short-run	0.99	0.28	0.30	0.03	0.41	*0.00*	0.02	*0.00*	0.84	0.68	0.06	0.05
Long-run	*0.00*	*0.00*	0.82	0.79	0.93	0.08	*0.01*	*0.00*	0.18	0.74	0.82	0.06
Overall	0.02	*0.00*	0.56	0.11	0.41	0.02	*0.00*	*0.00*	0.93	0.17	0.13	0.01
Japan
Short-run	0.99	*0.01*	0.54	0.37	0.14	*0.00*	0.73	0.38	0.84	0.59	0.23	0.12
Long-run	0.13	0.01	0.38	0.53	*0.01*	*0.00*	0.91	0.15	0.04	0.14	0.74	0.28
Overall	0.49	*0.00*	0.54	0.55	0.20	*0.00*	0.89	0.23	0.24	0.08	0.44	0.20
Sweden
Short-run	0.96	*0.00*	0.96	0.04	0.45	*0.00*	0.75	*0.00*	0.31	0.45	0.58	0.26
Long-run	0.03	0.03	0.12	0.52	0.22	*0.00*	0.07	*0.01*	0.25	0.74	0.32	0.05
Overall	0.14	*0.00*	0.47	0.13	0.29	*0.00*	0.23	*0.00*	0.51	0.43	0.49	0.06
United Kingdom
Short-run	0.64	0.12	0.13	0.02	0.10	0.03	0.03	*0.00*	0.59	0.35	*0.00*	0.02
Long-run	*0.00*	*0.00*	0.32	0.88	0.12	*0.00*	0.17	*0.01*	0.01	0.36	0.34	0.17
Overall	0.07	*0.00*	0.15	0.10	0.10	0.01	0.03	*0.00*	0.70	0.09	*0.01*	0.02

Source: Authors’ calculations. Note: Changes in interest rates and inflation expectations for each country are regressed on past levels and changes in interest rates and inflation expectations for the countries listed below and on past levels and changes in U.S. interest rates and inflation expectations. The regressions in Panel C do not include inflation expectations, p-values for three Wald tests are reported: (1) the exclusion of past changes in the dependent variables (short-run); (2) the exclusion of past levels of the dependent variables (long-run); and (3) the exclusion of both past changes in and past levels of the dependent variables (overall). Low p-values imply that the excluded variables are statistically significant determinants of current changes in interest rates or inflation expectations. Each panel contains four columns reporting, from left to right, results of the following tests: (1) the role of past U.S. variables in foreign markets; (2) the role of past domestic information in foreign markets; (3) the role of past foreign information in the U.S. market; and (4) the role of past domestic information in the U.S. market. All regressions contain contemporaneous and lagged changes in the VIX equity market volatility index as a control for risk aversion. Regressions for Japan begin in April, 2004. p-values reported in bold are significant at the 5 percent level; those reported in bold italics are significant at the 1 percent level.

To further explore the data, we also examined changes in yields from the close of one week to the close in the next week. As overlapping trading hours are much less of an issue, we use first lags for all series. The results, reported in Table 5, are quite similar to the daily data—real interest rate linkages run entirely from the United States to foreign markets. There is somewhat weaker evidence of spillovers in nominal bonds and inflation expectations in the opposite direction. It should be emphasized that the absence of significance of these tests does not imply that there are no links between markets, as the effects could occur contemporaneously. Thus, the possibility that foreign markets are of some importance for U.S. interest rates cannot be ruled out completely. However, these data establish that foreign markets do depend significantly on U.S. developments.

Table 5.

International Bond Market Spillovers at a Weekly Frequency

(p-values: January 4, 2002 to December 29, 2006)

Source: Authors’ calculations. Note: Changes in interest rates and inflation expectations for each country are regressed on past levels and changes in interest rates and inflation expectations for the countries listed below and on past levels and changes in U.S. interest rates and inflation expectations. The regressions in Panel C do not include inflation expectations, p-values for three Wald tests are reported: (1) the exclusion of past changes in the dependent variables (short-run); (2) the exclusion of past levels of the dependent variables (long-run); and (3) the exclusion of both past changes in and past levels of the dependent variables (overall). Low p-values imply that the excluded variables are statistically significant determinants of current changes in interest rates or inflation expectations. Each panel contains four columns reporting, from left to right, results of the following tests: (1) the role of past U.S. variables in foreign markets; (2) the role of past domestic information in foreign markets; (3) the role of past foreign information in the U.S. market; and (4) the role of past domestic information in the U.S. market. Regressions for Japan begin in April, 2004. p-values reported in bold are significant at the 5 percent level; those reported in bold italics are significant at the 1 percent level.

Table 5.

International Bond Market Spillovers at a Weekly Frequency

(p-values: January 4, 2002 to December 29, 2006)

	Real Interest Rates				Inflation Expectations				Nominal Interest Rates
	Foreign market		U.S. market		Foreign market		U.S. market		Foreign market		U.S. market
	United States	Domestic	Foreign	Domestic	United States	Domestic	Foreign	Domestic	United States	Domestic	Foreign	Domestic
Australia
Short-run	*0.00*	*0.00*	0.52	0.89	*0.00*	0.01	0.86	0.74	*0.00*	*0.00*	0.38	0.88
Long-run	0.10	0.01	0.19	0.13	0.02	*0.00*	0.54	0.23	*0.00*	0.11	0.16	0.43
Overall	*0.00*	*0.00*	0.22	0.34	*0.00*	*0.00*	0.80	0.46	*0.00*	*0.00*	0.17	0.73
Canada
Short-run	0.02	0.29	0.89	0.70	0.17	0.82	0.70	0.93	0.59	0.30	0.95	0.71
Long-run	*0.01*	*0.00*	0.23	0.22	0.03	*0.00*	0.17	0.78	0.17	0.35	0.05	0.04
Overall	*0.01*	*0.01*	0.49	0.45	0.06	*0.01*	0.38	0.94	0.34	0.40	0.11	0.09
France
Short-run	0.46	0.32	0.22	1.00	0.55	0.14	*0.01*	0.19	0.10	0.08	0.62	0.36
Long-run	0.01	*0.00*	0.79	0.34	0.49	0.08	*0.00*	*0.00*	0.05	0.93	0.14	0.09
Overall	0.03	*0.00*	0.37	0.65	0.51	0.08	*0.00*	*0.01*	0.25	0.06	0.38	0.13
Japan
Short-run	0.06	0.54	0.66	0.54	0.67	0.20	0.41	0.52	0.80	*0.01*	0.88	0.78
Long-run	*0.00*	*0.00*	0.44	0.47	0.01	0.02	0.62	0.15	0.00	0.02	0.54	0.55
Overall	*0.00*	0.01	0.37	0.70	0.07	0.04	0.79	0.24	*0.01*	0.06	0.82	0.80
Sweden
Short-run	0.08	0.43	0.98	0.89	0.43	*0.00*	0.20	0.44	0.16	0.02	0.81	0.48
Long-run	0.10	0.02	0.42	0.19	0.85	0.01	0.32	0.04	0.17	0.94	0.07	0.05
Overall	0.09	0.10	0.57	0.38	0.78	*0.00*	0.32	0.13	0.10	0.19	0.22	0.08
United Kingdom
Short-run	0.22	0.08	0.72	0.65	0.30	0.52	0.50	0.41	0.03	0.04	0.22	0.13
Long-run	0.04	*0.00*	0.28	0.30	0.36	0.04	0.33	0.13	0.01	0.73	0.07	0.25
Overall	0.03	*0.00*	0.54	0.47	0.55	0.19	0.56	0.28	0.18	*0.01*	0.13	0.19

Source: Authors’ calculations. Note: Changes in interest rates and inflation expectations for each country are regressed on past levels and changes in interest rates and inflation expectations for the countries listed below and on past levels and changes in U.S. interest rates and inflation expectations. The regressions in Panel C do not include inflation expectations, p-values for three Wald tests are reported: (1) the exclusion of past changes in the dependent variables (short-run); (2) the exclusion of past levels of the dependent variables (long-run); and (3) the exclusion of both past changes in and past levels of the dependent variables (overall). Low p-values imply that the excluded variables are statistically significant determinants of current changes in interest rates or inflation expectations. Each panel contains four columns reporting, from left to right, results of the following tests: (1) the role of past U.S. variables in foreign markets; (2) the role of past domestic information in foreign markets; (3) the role of past foreign information in the U.S. market; and (4) the role of past domestic information in the U.S. market. Regressions for Japan begin in April, 2004. p-values reported in bold are significant at the 5 percent level; those reported in bold italics are significant at the 1 percent level.

Table 5.

International Bond Market Spillovers at a Weekly Frequency

(p-values: January 4, 2002 to December 29, 2006)

	Real Interest Rates				Inflation Expectations				Nominal Interest Rates
	Foreign market		U.S. market		Foreign market		U.S. market		Foreign market		U.S. market
	United States	Domestic	Foreign	Domestic	United States	Domestic	Foreign	Domestic	United States	Domestic	Foreign	Domestic
Australia
Short-run	*0.00*	*0.00*	0.52	0.89	*0.00*	0.01	0.86	0.74	*0.00*	*0.00*	0.38	0.88
Long-run	0.10	0.01	0.19	0.13	0.02	*0.00*	0.54	0.23	*0.00*	0.11	0.16	0.43
Overall	*0.00*	*0.00*	0.22	0.34	*0.00*	*0.00*	0.80	0.46	*0.00*	*0.00*	0.17	0.73
Canada
Short-run	0.02	0.29	0.89	0.70	0.17	0.82	0.70	0.93	0.59	0.30	0.95	0.71
Long-run	*0.01*	*0.00*	0.23	0.22	0.03	*0.00*	0.17	0.78	0.17	0.35	0.05	0.04
Overall	*0.01*	*0.01*	0.49	0.45	0.06	*0.01*	0.38	0.94	0.34	0.40	0.11	0.09
France
Short-run	0.46	0.32	0.22	1.00	0.55	0.14	*0.01*	0.19	0.10	0.08	0.62	0.36
Long-run	0.01	*0.00*	0.79	0.34	0.49	0.08	*0.00*	*0.00*	0.05	0.93	0.14	0.09
Overall	0.03	*0.00*	0.37	0.65	0.51	0.08	*0.00*	*0.01*	0.25	0.06	0.38	0.13
Japan
Short-run	0.06	0.54	0.66	0.54	0.67	0.20	0.41	0.52	0.80	*0.01*	0.88	0.78
Long-run	*0.00*	*0.00*	0.44	0.47	0.01	0.02	0.62	0.15	0.00	0.02	0.54	0.55
Overall	*0.00*	0.01	0.37	0.70	0.07	0.04	0.79	0.24	*0.01*	0.06	0.82	0.80
Sweden
Short-run	0.08	0.43	0.98	0.89	0.43	*0.00*	0.20	0.44	0.16	0.02	0.81	0.48
Long-run	0.10	0.02	0.42	0.19	0.85	0.01	0.32	0.04	0.17	0.94	0.07	0.05
Overall	0.09	0.10	0.57	0.38	0.78	*0.00*	0.32	0.13	0.10	0.19	0.22	0.08
United Kingdom
Short-run	0.22	0.08	0.72	0.65	0.30	0.52	0.50	0.41	0.03	0.04	0.22	0.13
Long-run	0.04	*0.00*	0.28	0.30	0.36	0.04	0.33	0.13	0.01	0.73	0.07	0.25
Overall	0.03	*0.00*	0.54	0.47	0.55	0.19	0.56	0.28	0.18	*0.01*	0.13	0.19

Source: Authors’ calculations. Note: Changes in interest rates and inflation expectations for each country are regressed on past levels and changes in interest rates and inflation expectations for the countries listed below and on past levels and changes in U.S. interest rates and inflation expectations. The regressions in Panel C do not include inflation expectations, p-values for three Wald tests are reported: (1) the exclusion of past changes in the dependent variables (short-run); (2) the exclusion of past levels of the dependent variables (long-run); and (3) the exclusion of both past changes in and past levels of the dependent variables (overall). Low p-values imply that the excluded variables are statistically significant determinants of current changes in interest rates or inflation expectations. Each panel contains four columns reporting, from left to right, results of the following tests: (1) the role of past U.S. variables in foreign markets; (2) the role of past domestic information in foreign markets; (3) the role of past foreign information in the U.S. market; and (4) the role of past domestic information in the U.S. market. Regressions for Japan begin in April, 2004. p-values reported in bold are significant at the 5 percent level; those reported in bold italics are significant at the 1 percent level.

Further results from regressions using intraday data on nominal bond yields, contained in Bayoumi and Swiston (2007), also indicate strong evidence of U.S. spillovers to other markets and no evidence for spillovers in the other direction. Information from U.S. markets is significant in every case except Japan, and for several countries the coefficients on prices are insignificantly different from one, suggesting that U.S. news is incorporated one-for-one into foreign markets. Although the analysis covers a relatively short period—four-and-a-half months—these results are similar to those in Goldberg and Leonard (2003); Ehrmann and Fratzscher (2003, 2005); and Ehrmann, Fratzscher, and Rigobon (2007), who also find strong spillovers from U.S. interest rates to European rates but weak ones from Europe to the United States.

The analysis here presents strong evidence of spillovers from U.S. markets to foreign markets. The findings are most convincing with regard to real interest rates and weakest for inflation expectations. The tests for reverse causation show no evidence of spillovers to U.S. real interest rates but some evidence for nominal bonds and inflation expectations. Overall, these results are consistent with a world in which real interest rates are significantly determined by events in U.S. markets.

III. Quantifying Spillovers

We now move on to test the relative importance of bond spillovers across countries. Our results on efficiency suggest that spillovers for real interest rates and inflation expectations are somewhat different, so we focus on a specification using the daily data set that includes both of these components of nominal yields. Following on from the observation that our specification for testing the efficiency of markets was a reparameterization of a VAR in levels with two lags, we use such a VAR to quantify international spillovers. As the focus is on dynamic responses rather than the efficiency of the markets, first lags of U.S. yields are used. More specifically, the following VAR was estimated using data on the United States and each foreign market:

\begin{matrix} Z_{t} = A_{1} Z_{t - 1} + A_{2} Z_{t - 2} + ε_{t}, & (10) \end{matrix}

where Z_t is the vector (r_t, p_t, $r_{t}^{*}$ , $p_{t}^{*}$ ), the A vectors are coefficients, and ε_t is a vector of errors.

The order of the Cholesky decomposition requires discussion as, given significant contemporaneous correlations, it is central to the results. Owing to the predominance of spillovers from the United States to foreign markets, our base specification places the U.S. variables first in the ordering and foreign variables last—r_t, p_t, $r_{t}^{*}$ , $p_{t}^{*}$ . This assigns any contemporaneous correlation between U.S. and foreign variables to the United States, which appears to be justified given the results of Section III. Given the evidence that there could be feedback from foreign to U.S. markets with regard to inflation expectations, we also report an alternate specification. For the European and Canadian data, U.S. inflation expectations are placed last—r_t, $r_{t}^{*}$ , p_t, $p_{t}^{*}$ . For the Asian markets, as there is no overlap in trading, we ran $r_{t}^{*}$ , $p_{t}^{*}$ , r_t, p_t as the alternate ordering, with any contemporaneous correlation assigned to the Asian markets. Elsewhere, overlapping trading sessions make the appropriate ordering based on market trading times less clear, so r^US remains before r^*.¹³

We report the results of the VAR in terms of impulse response functions (IRFs, shown in Figures A1-A6 in the Appendix) and variance decompositions (Table 6). The IRFs indicate that U.S. real interest rates and inflation expectations are extremely close to a random walk. A one standard deviation shock to U.S. real rates moves them up by around 0.045 percent, with a very slight tendency to fall over the next 50 days. None of the other variables in the VARs—U.S. inflation expectations, foreign real rates, and foreign inflation expectations have any significant impact. U.S. inflation expectations show a similar profile, except the decay over time is more pronounced and there are some significant long-term effects from Australian and French variables.

Table 6.

Variance Decompositions after 50 Days

(Daily data from January 2, 2002 to December 29, 2006)

Source: Authors’ calculations. Note: The table shows the percent of the forecast error variance of the variables in each row attributed to innovations in the variable in each column, at a horizon of 50 days. The ordering in the Cholesky decomposition used to identify shocks to each variable is RUS, PUS, R^*, P^* in the left-hand panel and RUS, R^*, P^*, PUS in the right-hand panel. Alternate ordering for Australia and Japan is R^*, P^*, RUS, PUS. Regressions for Japan begin in April 2004. VAR = vector autoregression.

Table 6.

Variance Decompositions after 50 Days

(Daily data from January 2, 2002 to December 29, 2006)

		RUS, PUS, R^, P^						RUS, R^, P^, PUS
VAR Ordering Forecasted Variable		RUS	Percent attributed to		P^*	Forecasted Variable		RUS	Percent attributed to		P^*
VAR Ordering Forecasted Variable		RUS	PUS	R^*	P^*	Forecasted Variable		RUS	PUS	R^*	P^*
Australia						Australia
	RUS	95.9	0.2	0.1	3.8		RUS	90.2	0.2	1.5	8.1
	PUS	1.0	93.0	3.1	3.0		PUS	0.5	94.9	1.1	3.5
	R^*	29.7	8.1	59.0	3.2		R^*	23.2	4.6	70.4	1.8
	P^*	25.5	20.9	7.7	45.8		P^*	20.3	23.3	4.3	52.2
Canada						Canada
	RUS	98.1	0.1	0.0	1.8		RUS	98.1	0.5	0.0	1.5
	PUS	1.8	97.7	0.1	0.3		PUS	1.8	59.1	3.8	35.2
	R^*	44.3	4.1	50.9	0.8		R^*	44.3	7.8	46.5	1.4
	P^*	15.0	41.1	8.1	35.8		P^*	15.0	3.5	3.3	78.2
France						France
	RUS	99.8	0.1	0.0	0.1		RUS	99.8	0.0	0.0	0.1
	PUS	0.5	80.2	6.7	12.5		PUS	0.5	61.8	2.4	35.2
	R^*	58.7	1.0	37.2	3.1		R^*	58.7	4.8	35.2	1.4
	P^*	2.5	27.6	1.9	68.0		P^*	2.5	7.6	0.2	89.8
Japan						Japan
	RUS	96.3	0.1	0.0	3.5		RUS	94.8	0.1	2.0	3.1
	PUS	2.8	96.7	0.4	0.1		PUS	2.6	96.2	0.4	0.9
	R^*	35.8	4.6	47.0	12.7		R^*	25.8	4.2	57.1	12.9
	P^*	1.3	29.3	1.7	67.6		P^*	1.6	25.0	1.6	71.8
Sweden						Sweden
	RUS	98.9	0.9	0.2	0.1		RUS	98.9	0.7	0.2	0.2
	PUS	0.1	97.3	1.1	1.5		PUS	0.1	87.6	0.4	11.9
	R^*	37.7	1.2	58.6	2.5		R^*	37.7	2.8	58.0	1.5
	P^*	16.0	12.9	0.8	70.2		P^*	16.0	2.5	0.4	81.1
United Kingdom						United Kingdom
	RUS	96.5	0.5	1.8	1.3		RUS	96.5	0.4	2.1	1.0
	PUS	1.0	96.4	1.5	1.0		PUS	1.0	87.1	1.4	10.5
	R^*	32.3	2.3	60.2	5.2		R^*	32.3	7.2	57.6	2.9
	P^*	5.4	19.5	7.5	67.6		P^*	5.4	8.3	3.6	82.7
United States average						United States average
	RUS	97.6	0.3	0.4	1.8		RUS	96.4	0.3	1.0	2.3
	PUS	1.2	93.6	2.2	3.1		PUS	1.1	81.1	1.6	16.2
Foreign average						Foreign average
	R^*	39.7	3.5	52.1	4.6		R^*	37.0	5.2	54.1	3.6
	P^*	10.9	25.2	4.6	59.2		P^*	10.1	11.7	2.2	76.0

Table 6.

Variance Decompositions after 50 Days

(Daily data from January 2, 2002 to December 29, 2006)

		RUS, PUS, R^, P^						RUS, R^, P^, PUS
VAR Ordering Forecasted Variable		RUS	Percent attributed to		P^*	Forecasted Variable		RUS	Percent attributed to		P^*
VAR Ordering Forecasted Variable		RUS	PUS	R^*	P^*	Forecasted Variable		RUS	PUS	R^*	P^*
Australia						Australia
	RUS	95.9	0.2	0.1	3.8		RUS	90.2	0.2	1.5	8.1
	PUS	1.0	93.0	3.1	3.0		PUS	0.5	94.9	1.1	3.5
	R^*	29.7	8.1	59.0	3.2		R^*	23.2	4.6	70.4	1.8
	P^*	25.5	20.9	7.7	45.8		P^*	20.3	23.3	4.3	52.2
Canada						Canada
	RUS	98.1	0.1	0.0	1.8		RUS	98.1	0.5	0.0	1.5
	PUS	1.8	97.7	0.1	0.3		PUS	1.8	59.1	3.8	35.2
	R^*	44.3	4.1	50.9	0.8		R^*	44.3	7.8	46.5	1.4
	P^*	15.0	41.1	8.1	35.8		P^*	15.0	3.5	3.3	78.2
France						France
	RUS	99.8	0.1	0.0	0.1		RUS	99.8	0.0	0.0	0.1
	PUS	0.5	80.2	6.7	12.5		PUS	0.5	61.8	2.4	35.2
	R^*	58.7	1.0	37.2	3.1		R^*	58.7	4.8	35.2	1.4
	P^*	2.5	27.6	1.9	68.0		P^*	2.5	7.6	0.2	89.8
Japan						Japan
	RUS	96.3	0.1	0.0	3.5		RUS	94.8	0.1	2.0	3.1
	PUS	2.8	96.7	0.4	0.1		PUS	2.6	96.2	0.4	0.9
	R^*	35.8	4.6	47.0	12.7		R^*	25.8	4.2	57.1	12.9
	P^*	1.3	29.3	1.7	67.6		P^*	1.6	25.0	1.6	71.8
Sweden						Sweden
	RUS	98.9	0.9	0.2	0.1		RUS	98.9	0.7	0.2	0.2
	PUS	0.1	97.3	1.1	1.5		PUS	0.1	87.6	0.4	11.9
	R^*	37.7	1.2	58.6	2.5		R^*	37.7	2.8	58.0	1.5
	P^*	16.0	12.9	0.8	70.2		P^*	16.0	2.5	0.4	81.1
United Kingdom						United Kingdom
	RUS	96.5	0.5	1.8	1.3		RUS	96.5	0.4	2.1	1.0
	PUS	1.0	96.4	1.5	1.0		PUS	1.0	87.1	1.4	10.5
	R^*	32.3	2.3	60.2	5.2		R^*	32.3	7.2	57.6	2.9
	P^*	5.4	19.5	7.5	67.6		P^*	5.4	8.3	3.6	82.7
United States average						United States average
	RUS	97.6	0.3	0.4	1.8		RUS	96.4	0.3	1.0	2.3
	PUS	1.2	93.6	2.2	3.1		PUS	1.1	81.1	1.6	16.2
Foreign average						Foreign average
	R^*	39.7	3.5	52.1	4.6		R^*	37.0	5.2	54.1	3.6
	P^*	10.9	25.2	4.6	59.2		P^*	10.1	11.7	2.2	76.0

By contrast, foreign variables appear subject to significant spillovers from U.S. markets. Domestic shocks in foreign real rates are smaller than in the United States, varying between 0.015 and 0.03 percent, but these are augmented by spillovers from U.S. real interest shocks that vary between 0.01 to 0.025 percent. In round figures, between one-quarter and one-half of U.S. real interest rate shocks are transmitted to foreign markets. These shocks account for a similar proportion of movements in foreign real rates. Finally, changes in U.S. inflation expectations generally have a temporary positive impact on real rates abroad.

Foreign inflation expectations have similarly sized own shocks to foreign real interest rates (0.015 to 0.03 percent). They also generally exhibit significant positive spillovers from both U.S. inflation expectations and (to a somewhat lesser extent) U.S. real rates. Finally, they are usually negatively affected by shocks to local real rates. One interpretation of the divergent signs with regard to spillovers from U.S. and domestic real rates is that increases in U.S. real rates are seen as a precursor of global inflation pressures (hence the positive relationship) but higher domestic real rates are seen as a reflection of monetary tightening, and hence lower expected inflation in the future.

The variance decomposition in Table 6 reports the importance of each shock in the outcome of each variable after 50 days. The results in the left columns, which use the base Cholesky decomposition, confirm that outcomes for U.S. real rates and inflation expectations are dominated by local shocks. By contrast, 20 to 60 percent of foreign real rate variances are determined by U.S. real interest rate shocks, with most of the rest reflecting domestic real interest rate shocks—U.S. and domestic inflation expectations generally play only a minor role.¹⁴ A similar quantitative pattern holds for foreign inflation expectations, except U.S. spillovers involve both U.S. inflation expectations and, to a lesser extent, U.S. real rates.

Results using the alternative Cholesky decompositions are reported in Figures A7-A12 in the Appendix and the right half of Table 6. Unsurprisingly, results for U.S. real rates remain essentially unchanged. Foreign inflation expectations now play a more important role in determining U.S. inflation expectations, although there continues to be evidence of U.S. spillovers, particularly from real rates, to foreign real rates and inflation expectations even under this specification.

An important concern about the VARs using daily data is that the time frame over which the results are projected is only 50 days, a relatively short period for macroeconomic analysis. To analyze the responses over somewhat longer periods, we repeated the VAR analysis using end-week data. The results of the IRFs (not shown for the sake of brevity) indicate that the patterns seen in the daily data are also true for longer periods. Indeed, as can be seen from the variance decompositions for these VARs reported in Table 7, the importance of spillovers appears to rise over longer horizons. After a year, U.S. factors on average comprise more than half of the variation in foreign real interest rates (aside from an anomalous result for Australia, where the importance declines to 2 percent, from 23 percent in the daily data), and spillovers from U.S. to foreign inflation expectations also rise.

Table 7.

Variance Decompositions after One Year

(Weekly data from January 4, 2002 to December 29, 2006)

Source: Authors’ calculations. Note: The table shows the percent of the forecast error variance of the variables in each row attributed to innovations in the variable in each column, at a horizon of 52 weeks. The ordering in the Cholesky decomposition used to identify shocks to each variable is RUS, PUS, R^*, P^* in the left-hand panel and RUS, R^*, P^*, PUS in the right-hand panel. Alternate ordering for Australia and Japan is R^*, P^*, RUS, PUS. Regressions for Japan begin in April 2004. VAR = vector autoregression.

Table 7.

Variance Decompositions after One Year

(Weekly data from January 4, 2002 to December 29, 2006)

		RUS, PUS, R^, P^						RUS, R^, P^, PUS
VAR Ordering Forecasted Variable		RUS	Percent attributed to		P^*	Forecasted Variable		RUS	Percent attributed to		P^*
VAR Ordering Forecasted Variable		RUS	PUS	R^*	P^*	Forecasted Variable		RUS	PUS	R^*	P^*
Australia						Australia
	RUS	85.4	4.0	3.9	6.6		RUS	58.2	4.6	12.9	24.3
	PUS	6.5	87.5	3.9	2.0		PUS	6.1	88.5	3.2	2.2
	R^*	21.2	11.2	65.9	1.7		R^*	1.8	16.5	78.1	3.5
	P^*	17.6	19.8	38.5	24.1		P^*	8.1	22.2	14.2	55.5
Canada						Canada
	RUS	81.3	9.9	0.9	7.8		RUS	81.3	0.8	1.4	16.5
	PUS	12.4	80.9	0.4	6.4		PUS	12.4	69.4	1.7	16.6
	R^*	44.8	31.5	16.9	6.8		R^*	44.8	38.7	14.1	2.4
	P^*	13.8	59.8	4.0	22.4		P^*	13.8	26.1	2.6	57.5
France						France
	RUS	95.4	1.1	0.1	3.5		RUS	95.4	0.3	0.0	4.3
	PUS	9.2	73.8	13.9	3.1		PUS	9.2	36.4	7.8	46.6
	R^*	77.6	1.1	16.4	4.8		R^*	77.6	6.3	15.4	0.7
	P^*	2.9	51.5	8.4	37.2		P^*	2.9	5.1	3.9	88.1
Japan						Japan
	RUS	79.0	1.2	7.1	12.7		RUS	85.8	3.5	4.4	6.4
	PUS	2.8	91.0	5.5	0.7		PUS	6.4	87.7	3.3	2.6
	R^*	56.1	4.2	23.6	16.1		R^*	56.7	1.2	29.3	12.8
	P^*	3.8	35.6	13.0	47.5		P^*	12.2	17.2	9.1	61.4
Sweden						Sweden
	RUS	90.8	5.2	0.1	3.9		RUS	90.8	1.3	0.3	7.6
	PUS	6.8	88.9	4.2	0.1		PUS	6.8	73.7	1.3	18.2
	R^*	60.8	3.4	31.6	4.2		R^*	60.8	8.4	29.8	1.1
	P^*	21.8	23.1	6.0	49.1		P^*	21.8	2.5	4.1	71.6
United Kingdom						United Kingdom
	RUS	85.0	1.9	11.2	1.9		RUS	85.0	0.6	12.5	1.9
	PUS	6.2	89.7	3.8	0.3		PUS	6.2	64.1	0.7	29.0
	R^*	41.3	5.0	28.6	25.1		R^*	41.3	24.2	26.9	7.6
	P^*	5.3	46.9	19.3	28.6		P^*	5.3	16.5	9.8	68.4
United States average						United States average
	RUS	86.2	3.9	3.9	6.0		RUS	82.8	1.8	5.3	10.2
	PUS	7.3	85.3	5.3	2.1		PUS	7.8	70.0	3.0	19.2
Foreign average						Foreign average
	R^*	50.3	9.4	30.5	9.8		R^*	47.2	15.9	32.3	4.7
	P^*	10.9	39.5	14.9	34.8		P^*	10.7	14.9	7.3	67.1

Source: Authors’ calculations. Note: The table shows the percent of the forecast error variance of the variables in each row attributed to innovations in the variable in each column, at a horizon of 52 weeks. The ordering in the Cholesky decomposition used to identify shocks to each variable is RUS, PUS, R^*, P^* in the left-hand panel and RUS, R^*, P^*, PUS in the right-hand panel. Alternate ordering for Australia and Japan is R^*, P^*, RUS, PUS. Regressions for Japan begin in April 2004. VAR = vector autoregression.

Table 7.

Variance Decompositions after One Year

(Weekly data from January 4, 2002 to December 29, 2006)

		RUS, PUS, R^, P^						RUS, R^, P^, PUS
VAR Ordering Forecasted Variable		RUS	Percent attributed to		P^*	Forecasted Variable		RUS	Percent attributed to		P^*
VAR Ordering Forecasted Variable		RUS	PUS	R^*	P^*	Forecasted Variable		RUS	PUS	R^*	P^*
Australia						Australia
	RUS	85.4	4.0	3.9	6.6		RUS	58.2	4.6	12.9	24.3
	PUS	6.5	87.5	3.9	2.0		PUS	6.1	88.5	3.2	2.2
	R^*	21.2	11.2	65.9	1.7		R^*	1.8	16.5	78.1	3.5
	P^*	17.6	19.8	38.5	24.1		P^*	8.1	22.2	14.2	55.5
Canada						Canada
	RUS	81.3	9.9	0.9	7.8		RUS	81.3	0.8	1.4	16.5
	PUS	12.4	80.9	0.4	6.4		PUS	12.4	69.4	1.7	16.6
	R^*	44.8	31.5	16.9	6.8		R^*	44.8	38.7	14.1	2.4
	P^*	13.8	59.8	4.0	22.4		P^*	13.8	26.1	2.6	57.5
France						France
	RUS	95.4	1.1	0.1	3.5		RUS	95.4	0.3	0.0	4.3
	PUS	9.2	73.8	13.9	3.1		PUS	9.2	36.4	7.8	46.6
	R^*	77.6	1.1	16.4	4.8		R^*	77.6	6.3	15.4	0.7
	P^*	2.9	51.5	8.4	37.2		P^*	2.9	5.1	3.9	88.1
Japan						Japan
	RUS	79.0	1.2	7.1	12.7		RUS	85.8	3.5	4.4	6.4
	PUS	2.8	91.0	5.5	0.7		PUS	6.4	87.7	3.3	2.6
	R^*	56.1	4.2	23.6	16.1		R^*	56.7	1.2	29.3	12.8
	P^*	3.8	35.6	13.0	47.5		P^*	12.2	17.2	9.1	61.4
Sweden						Sweden
	RUS	90.8	5.2	0.1	3.9		RUS	90.8	1.3	0.3	7.6
	PUS	6.8	88.9	4.2	0.1		PUS	6.8	73.7	1.3	18.2
	R^*	60.8	3.4	31.6	4.2		R^*	60.8	8.4	29.8	1.1
	P^*	21.8	23.1	6.0	49.1		P^*	21.8	2.5	4.1	71.6
United Kingdom						United Kingdom
	RUS	85.0	1.9	11.2	1.9		RUS	85.0	0.6	12.5	1.9
	PUS	6.2	89.7	3.8	0.3		PUS	6.2	64.1	0.7	29.0
	R^*	41.3	5.0	28.6	25.1		R^*	41.3	24.2	26.9	7.6
	P^*	5.3	46.9	19.3	28.6		P^*	5.3	16.5	9.8	68.4
United States average						United States average
	RUS	86.2	3.9	3.9	6.0		RUS	82.8	1.8	5.3	10.2
	PUS	7.3	85.3	5.3	2.1		PUS	7.8	70.0	3.0	19.2
Foreign average						Foreign average
	R^*	50.3	9.4	30.5	9.8		R^*	47.2	15.9	32.3	4.7
	P^*	10.9	39.5	14.9	34.8		P^*	10.7	14.9	7.3	67.1

Source: Authors’ calculations. Note: The table shows the percent of the forecast error variance of the variables in each row attributed to innovations in the variable in each column, at a horizon of 52 weeks. The ordering in the Cholesky decomposition used to identify shocks to each variable is RUS, PUS, R^*, P^* in the left-hand panel and RUS, R^*, P^*, PUS in the right-hand panel. Alternate ordering for Australia and Japan is R^*, P^*, RUS, PUS. Regressions for Japan begin in April 2004. VAR = vector autoregression.

IV. Conclusions

This paper has used data on inflation-indexed bonds to examine domestic and international spillovers across countries. Given the dominant position of the United States in global bond markets—U.S. markets comprise almost two-thirds of all private bond trading—the focus has been on links between the United States and other major industrial countries with inflation-indexed bonds (Australia, Canada, France—which can be seen as a proxy for the euro area—Japan, Sweden, and the United Kingdom).

Using a variety of techniques, a relatively uniform picture emerges:

Real interest rates appear much more linked across countries than the corresponding inflation expectations, exactly as would be expected given that real rates are more likely to be affected by global factors while inflation expectations depend more on domestic events.
Real interest rate spillovers flow exclusively from the United States to other countries, and U.S. markets appear to efficiently absorb available information, in contrast to their foreign counterparts. Tests indicate that U.S. factors on average determine about one-half of foreign real interest rates and that, if anything, this proportion rises over time.
There are smaller international spillovers in inflation expectations, with the results again suggesting that U.S. spillovers tend to be the most important but with more evidence of reverse causation. U.S. market developments account for a quarter to a third of fluctuations in foreign inflation expectations, while reverse spillovers generally account for a smaller proportion of U.S. forecasts, although the exact results depend on the chosen specification.
Spillovers from the United States to Japan are similar to those for other countries. The absence of an active monetary policy, given that the Japanese had a zero interest rates over most of the sample period, does not appear to have materially affected the transition mechanism across international bond markets.

In addition to confirming the dominant position of U.S. bond markets in global yields, these results illuminate the underlying sources of these links. In particular, it makes perfect sense that U.S. markets are a major factor in determining global real rates, which should involve arbitrage across destinations, while inflation expectations—which are more domestically determined—are less integrated internationally and involve more complex dynamics. In addition, while U.S. developments are clearly crucial to global bond markets given the importance of its economy and financial markets, U.S. bond yields can and do also reflect international developments, such as the global “saving glut.” Deep and liquid U.S. bond markets are hence also central to global price discovery for long-term real rates.

Given the importance of long-term real interest rates in determining activity, these financial spillovers clearly represent an extremely important conduit from the United States to other industrial countries, particularly as real bond yields are also a key driver of the valuations of many other financial instruments, such as equities.

Appendix

Figures A1-A12 show impulse-response functions up to a horizon of 50 days. Interest rates and inflation expectations are expressed in percentage points. The figures show the response, in percentage points, of the first variable listed to a one standard deviation shock in the second variable listed. The ordering of the Cholesky decomposition used to identify shocks to each variable is RUS, PUS, R^*, P^* in Figures A1-A6; RUS, R^*, P^*, PUS in Figures A8, A9, A11 and A12; and R^*, P^*, RUS, PUS in Figures A7 and A10.

Figure A1.

Impulse-Response Functions, Australia

Citation: IMF Staff Papers 2010, 002; 10.5089/9781589069121.024.A004