Data and Stationarity Test

This section describes the time-series daily yield data from different bond markets applied in the current study. Price data relating federal funds futures contracts, as well as ten-year Treasury futures contracts, are used to calculate both short- and long-term U.S. QE policy surprises (the independent variable), respectively. Some control and dummy variables are included in the estimation.

3.2.1

Data

This study covers the period from the 1st of January 2007 to the 31st of December 2015, which includes all three of the Fed’s QE periods; U.S. QE1 covers the 25th of November 2008 through the 25th of March 2010, U.S. QE2 covers the 3rd of November 2010 to the 25th of June 2011, and U.S. QE3 covers from the 13th of September 2012 to the 29th of October 2014. The bond yield data were obtained from Bloomberg and DataStream. The daily data applied in this current study includes the federal funds futures data, the ten-year Treasury futures data, the ten-year government bond yields from ten bond markets, and the price data from international stock markets. Daily data was chosen because it provides more information about the immediate responses to exogenous shocks which typically only last for a couple of days rather than relying on weekly and monthly data (Gallagher & Twomey, 1998; Worthington & Higgs, 2004).

The first data set contains information about on the 30 days Federal funds futures contract or more specifically, tracks the overnight Federal funds rate for each month (Kishor & Marfatia, 2013). It is calculated with 100 minus the expected average effective Federal funds rate for the delivery month. This data is used by the current study to calculate short-term U.S. monetary policy shocks generated by the U.S. monetary policies. In addition to the measurement of short-term U.S. policy shocks, I also measure the long-term U.S. monetary policy shocks using the ten-year Treasury futures data. Short- and long-term U.S. monetary policy shocks that correspond to each QE period are generated by multiplying short-and long-term U.S. monetary policy shocks by a dummy variable which represents each individual U.S. QE round (see section 3.3).

Another data set consists of the daily bond yield data from ten long-term (ten-year) government bond markets based on Fratzscher et al. (2018) and Kishor and Marfatia (2013) study. Of all the assets purchased by the Federal Reserves within the U.S. QE policy framework, the largest purchase was on long-term government bonds, and in particular, the ten-year bonds (Gagnon et al., 2010; Neely, 2015). It is for this reason that the current study chooses to focus on these bonds to evaluate QE impacts.

I include some variables to control for changes in both international and domestic economic environments in our study. Since the data used in this study is daily, common macroeconomic variables such as inflation rate and GDP growth are difficult to include. Unlike financial market data, which is available daily or at even higher frequencies, macroeconomic data is usually released monthly, or sometimes quarterly. This means it is challenging to include macroeconomic variables in financial models which use daily based data. However, it is still possible to incorporate changes in economic environments using daily data. The most readily available proxy variable adopted in the previous study (Steeley & Matyushkin, 2015) is the stock market return. I include return data from each sample stock markets as a control for the changes in the stock performance. Apart from daily stock returns, the lag value of bond yields are also incorporated to represent previous information generated within each bond market.

All markets in the study sample are divided into developed markets and emerging markets according to Fratzscher et al. (2018) study, as shown in Table 3.1. The comparison of responses from different groups will provide more detailed information on how the global bond markets respond to the U.S. unconventional monetary policies. The six developed markets include the United States (US), the United Kingdom (UK), Japan (JP), Australia (AU), France (FR) and Germany (GE). The emerging markets included in this study are China (CH), Brazil (BR), India (IND), and Russia (RU). They are markets that either have great impact on the global economy, that is the U.S., the U.K. and Japan

(Yang, 2005) or ones which play a more pronounced role in the global markets such as Brazil, Russia, India and China (BRIC markets). In addition to these markets, I also include bond yields from other markets. I consider bond yields from Hong Kong, Canada and New Zealand for developed markets. In terms of emerging markets, I include Pakistan, South Africa, Thailand, and Malaysia. However, due to missing data, especially for some essential U.S. QE starting and ending dates, I exclude these markets. For example, there are 1893 data for Hong Kong market and the entire sample size is 2349. Moreover, there is still a debate on the definition of emerging markets. For instance, Malaysia is not in the group of BRICS+ Next Eleven markets nor in the Columbia University Emerging Market Global Player (EMGP) groups. Pakistan is not accepted by S&P, Dow Jones and Russell Investment in the emerging markets. Indonesia is not on the Columbia University EMGP list and Thailand is not in the BRICS+ Next Eleven. Therefore, I only choose the BRIC markets, the four largest and well-known emerging markets for my study.

Table 3-1 Markets Included in the Current Study

Developed Market Emerging Market

United States (US) China (CH)

United Kingdom (UK) Brazil (BR)

Japan (JP) India (IN)

Australia (AU) Russia (RU)

France (FR) Germany (GE)

Based on (Fratzscher et al., 2018; Kishor & Marfatia, 2013)

3.2.2

Stationarity of Data and Break Points

The stationary series is the one with a constant mean, variance and auto-covariance for each given lag. In other word, the stationary series has all these statistical properties with constant over time. This is very different from non-stationary variables, which have time dependent means and covariance. A random process time series is integrated in the order d; in the series the random process requires a difference of d time in order to guarantee stationarity (Engle & Granger, 1987). It is necessary to test for stationarity in time series data before running a regression analysis because there will be spurious regression results when running traditional regression analysis with non- stationary time series variables (Granger & Newbold, 1974). The R2 _{may be high and the t statistics}

may be significant for a spurious regression result, but the results are meaningless statistically. In short, the output will appear significant due to the non-consistent least squares estimates and the t

statistics do not follow the normal t distribution. Therefore, the integration properties of the data should be examined in advance of any regression analysis. In this study, I use the Augmented Dickey Fuller (ADF) test, Dickey Fuller Generalized Least Square (DFGLS) test, Phillips-Perron (PP) test and Break Point Unit Root test, respectively. Specifically, I run the tests for both the level and first- difference of the bond yield data.

Besides the unit root tests, based on different U.S. QE programs, I also run the break point tests to examine the potential structural break dates in the bond yield series. In addition to the Break Point Unit Root test discussed in section 3.2.2, I also apply the Chow test to examine if the key U.S. QE announcement dates (Including the starting and ending dates of each U.S. QE policy) are the potential structural break points for the sample series.