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Economic Diversification and the State of Oil Dependency of UAE Stock Returns-An Analysis of ADX Indices 2014-2019

Impact of commodity price risk on stock return remains an important forecasting parameters across stock markets of developed and emerging markets. In recent times the subdued oil price poses a challenge to the economic imbalance among oil producing countries, and thus non-oil diversification has been adopted as an economic solution. Amongst the GCC countries, the intensity of non-oil diversification has been found to be higher in the UAE which prompted to conduct a separate study of impact of oil price volatility on stock returns of Abu Dhabi Securities Market General Index and various sectoral indices. This study examines whether UAE stock returns are still associated with changes in oil price as reported in earlier research despite significant improvements in non-oil sector GDP contributions. The empirical assessment is based on weekly returns of the Abu Dhabi Stock Market General Index and four sectoral indices, namely, banking, industrial, energy and real estate in relation to variations in weekly WTI prices for the period between 1 week of 2012 to 29 week of 2019, i.e., for a period of 392 weeks applying Vector Error Correction model and Granger Causality test. It is found that there exists both long run and short run association between oil price volatility and stock return except model misspecification in respect of industrial and energy sectors arising out of serial correlation. Two lagged weekly oil price movements are found to be strong explanatory variables of stock returns.

However, non-oil sectors advanced at a softer pace; growing by 1.3% in 2018 compared to a growth of 1.9% in the previous year. Softer pace of growth was a reflection of the slowdown in some of the non-oil sectors [34]. Detailed of on non-oil sector growth in the UAE is presented in Table 1.
Diversification efforts combined with fiscal reforms of reduced subsidies for fuel and electricity and new taxes and fees have failed to counterbalance the fall in oil revenues. Thus, the UAE has set the non-oil GDP growth as an important key performance indicator in Vision 2021. The UAE Government approved an AED 50 billion (USD13.6 billion) economic stimulus package, with a fund of AED 20 billion (USD5.4 billion) allocated to the 2019 development package. This package aims at further reducing oil dependency of the UAE economy encouraging establishment of new industries and attracting foreign investments. The package includes ten economic initiatives including Abu Dhabi Accelerators and Advanced Industries Council to support the generation of more business activities and achieve higher share of private sector economic activity and to address the structural bottlenecks.  (2018) In view of the non-oil diversification efforts of the UAE government and resulting increases in contribution of non-oil sectors to the GDP, this study aims at evaluating whether the UAE has been successful in decoupling its economic performance from oil price fluctuations. The stock market being an important barometer of economic performance, any sign of economic decoupling should be identifiable through the movement of stock market indices vis a vis oil price movement. Based on this theorem, a stream of empirical research has used the co-integration of stock market movement and oil price as a sign of oil dependency. Researchers have also evaluated whether oil price movement "Granger causes movement in stock market indices".
This study is uniquely based on the Abu Dhabi Securities Market (ADX) general index and sectoral indices on the background of its non-oil diversification effort rather than general studies of GCC countries wherein non-oil diversification is of relatively higher. An IMF staff paper [ Olumuyiwa et al (2018)] described that GCC countries are differently impacted by lower oil price and the policy makers of various GCC countries differently attempted to address lower oil price. They observed that only the UAE could broadly balance between increases in revenues and restraint in spending. Also the UAE has been focusing for deepening the knowledge-driven economy, and has taken initiatives to increase competition, improve energy efficiency, and promotion of entrepreneurship. Cheikh et al [2018] documented heterogeneous reactions of stock markets across GCC countries to oil price change. They found significant asymmetries in the relationships between oil prices and stock markets in some GCC nations (Kuwait, Oman, and Qatar), but not in others (Bahrain, Saudi Arabia, and the UAE). This study draws motivation from these findings to conduct a separate study based on the Abu Dhabi stock market data because of its distinct non-oil diversification measures. Also the study period has been matched to the period of non-oil diversification in the UAE. Figure 3 presents co-movement of weekly ADXG return and weekly change in WTI oil price (US$) per barrel. Although strong sign of covariance has been observed between weekly return of stock indices and oil price change, post-2014 covariance is found to be weakening compared to covariance during 2007-2011 which may be considered as an early signal of decoupling of stock market volatility from oil price volatility. Induced by this early signal, this research study intends to assess whether non-oil diversification efforts that substantially changed the GDP structure of UAE helped to insulate the UAE stock market from the vagaries of oil market volatility.
Data Sources: www.adx.com and https://www.investing.com/currencies/wti-usd-historical-data ; calculation by author Applying Vector Error Correction model and Granger Causality tests, it has been established that non-oil diversification could not decouple UAE stock returns. This study is based on data of Abu Dhabi Stock Exchange. Dubai Financial Market data are not mixed up in this analysis since oil dependency of Dubai emirate of the UAE is quite different. A recent Working Paper of IMF (2018) explains that that Saudi Arabia's equity market movements have a statistically significant impact on the equity markets in the rest of the GCC countries, after controlling for oil prices and global market developments. Specifically, a one percentage point increase in Saudi equity market returns is associated with a 0.06 percentage point increase in the rest of the GCC equity returns in the subsequent day. This study has not taken into account 'Saudi Arabia spillover effect' which is proposed to be covered in a separate research.
The layout of this paper is as follows: Section 2 covers a brief summary of relevant literature; data and methodology are explained in Section 3; Section 4 covers data analysis and Section 5 contains concluding remarks covering limitations and scope for further research.

Literature Review
Hamilton (2013) surveyed key post-World War II oil price shocks covering Suez Crisis of 1956-57, the OPEC oil embargo of 1973-1974, the Iranian revolution of 1978-1979, the Iran-Iraq War initiated in 1980, the first Persian Gulf War in 1990-91, the oil price spike of 2007-2008, and also other minor disturbances. His research underpinned the understanding of economic consequences of oil price shocks. Earlier Hamilton (1983Hamilton ( , 1996Hamilton ( ,2009) studied the differential impact of oil price shocks on US economies and policy implications thereof. In particular, his research inter alia highlighted why US consumers responded so little when the price of oil moved up from $41 per barrel in July 2004 to $65 in August 2005 (a 59% increase), but they responded quite differently to increase in oil price from $72 in August 2007 to $134 (an 86% increase) in June 2008.
Also, the growing body of literature provided evidence on varied features of empirical relationship between oil price shocks and GDP. Hamilton (1983) found a statistically significant relationship between changes in oil prices and changes in real GNP and unemployment in the US economy during 1948-1973. He observed that seven out of the previous eight recessions had been preceded by a dramatic increase in crude oil prices. Mork (1989) found that oil price increases have more impact on economy than oil price decreases. He expanded on Hamilton's (1983) study by incorporating data from the 1980s into his analysis and found that positive oil price shocks had negative effects on output, while negative oil price shocks did not have expansionary effects on output. His further work [ Mork et al (1994)] highlighted the economic responses to both positive and negative oil price shocks in seven OECD countries and showed that correlations with positive oil price shocks and output were negative and significant for most of the countries, while correlations with negative oil price shocks were positive. Dotsey and Reid (1992) observed that oil price change impacted GDP by 5-6%. Hooker (1996) also confirmed Hamilton's results and indicated that oil price changes had negative effects on the growth of US GDP during the period between 1948-1972. He observed that the OPEC price increases had significant impacts, while the effects of the price declines of the 1980s are smaller and harder to characterize. These results have potentially important implications for the large body of research which utilizes oil prices as an instrumental or explanatory variable.
Following the works by Chen et al (2018) that identified oil price movement as a risk factor for stock price and of Jones and Kaul (1996) that analyzed the reaction of international stock markets, a substantial body of research work examined the effect of change in oil price on stock return. They examined the impact of oil price change on shocks in stock markets in the US, Canada, UK, and Japan. They concluded that the effects of oil shocks on the US and Canadian stock markets can be explained by their effects on current and future real cash flows. However, real cash flows and expected return proxies could not explain the fluctuations on the stock markets in Japan and the UK. The postwar oil shocks seemed to have generated volatility in the stock markets. Sadorsky (1999) found that post-1986 oil price movements explain a larger fraction of the forecast error variance in real stock returns than do interest rates. He observed that oil price volatility shocks have asymmetric effects on the economy. Sadorsky (1999) showed that an oil price shock has a negative and statistically significant initial impact on stock returns. In another paper, Basher and Sadorsky (2006) studied the impact of oil price changes on a large set of emerging stock market returns and found strong evidence oil price risk impact on stock return in emerging markets.
Using a multivariate vector-autoregression approach, Papapetrou (2001) attempted to explain the dynamic relationship among oil prices, real stock prices, interest rates, real economic activity and employment in Greece. He observed that changes in oil price affect real economic activity and employment. Also, oil prices are important in explaining stock price movements. Hammoudeh and Li (2005) found a positive association between oil prices and equity returns with respect to oil producing countries, but a negative association with the broad-based MSCI World Index. They examined and compared the oil sensitivity of equity return of non-Gulf, oil producing countries (e.g. Mexico and Norway) and two major oil-sensitive industries of the US (e.g. oil and transportation). They concluded that the oil price growth leads the stock returns of the oil-exporting countries and the US oil-sensitive industries. Thus, investors view the systematic risk more importantly than the oil sensitivity in pricing those oil-sensitive returns, regardless of the direction of the world capital market. By applying Vector Autoregression (VAR) models and bivariate Granger causality tests, Feride (2015) showed that both symmetric and positive oil price shocks decrease industrial production, money supply, and imports while the negative oil price shocks increase imports. Sonenshine and Cauvel (2017) explored how the magnitude of crude oil price changes affect the stock market returns and variances of key production, banking and consuming segments of the US economy. They provided explanations for the asymmetric responses to positive and negative oil shocks found in key sectors of the US economy.
In the context of stock markets of GCC countries, Maghyereh and Al-Kandari (2007) showed that in the long-run oil prices impact the stock price indices. Arouri et al (2010) examined short-term links between oil prices and stock markets in GCC countries using data from June 2005 to October 2008. They found that stock market returns react significantly to oil price changes in Qatar, Oman, Saudi Arabia, and the UAE. Also, relationships between oil prices and stock markets in these countries are nonlinear and switch according to the oil price values. However, for Bahrain and Kuwait they found that oil price changes do not affect stock market returns. Alhayki (2014) examined the impact of oil price on stock market returns of GCC countries by applying wavelet analysis model on monthly data from May 2005 to December 2011. The results of Granger causality of MODWT multi-resolution analysis show that in the long run a strong bidirectional causal relationship exists between oil prices and each of the stock market returns in the GCC region. Using recent bootstrap panel cointegration techniques and seemingly unrelated regression (SUR) methods, Arouri and Rault (2012) observed that there is evidence for cointegration between oil prices and stock markets in GCC countries, while the SUR results indicate that oil price increases have a positive impact on stock prices, except in Saudi Arabia.
Alqattan and Alhayky (2016) studied the relationship between oil prices and the stock market price in GCC for the period between 2006-2015 and found that oil price fluctuations play an important role in determining the stock market prices in GCC countries in the short run. This study also concluded that in the long run stock market price is not sensitive to oil price fluctuations in GCC countries except in Oman. Dutta et al. (2017) report a positive, significant relationship between oil prices and realized stock market uncertainties even after controlling for global stock market uncertainty in Saudi Arabia, Kuwait, the UAE, and Qatar. Applying Johansen Cointegration test on Box Cox transformed data of oil price and seven stock market indices of GCC countries, Ghosh ( 2017) found that oil price and GCC stock markets are co-integrated. This study explained that efforts to reduce oil dependency in GCC countries is yet to result in decoupling of financial markets from oil price cyclicality. Vohra (2017) explained the oil dependency of GCC economies and showed that there is a link between economic growth and oil price changes, in particular to the current account balances of GCC countries. Cheikh et al. (2018) observed the presence of stock market returns' asymmetric reactions in some GCC countries, but not for others. They found that negative oil price changes exert larger impacts on stock returns than positive oil price changes in Kuwait's case. When considering the asymmetry with respect to the magnitude of oil price variation, they found that Oman's and Qatar's stock markets are more sensitive to large oil price changes than to small ones.

Research Hypothesis and Study Period
This study intends to test whether UAE stock returns are still associated with changes in oil price despite improvements in non-oil sector GDP contributions. The change stock return of a week is attempted to be explained by oil price changes in earlier week(s) and also stock returns of earlier week(s). In Section 3.4, VAR lag order selection has been explained. Explanatory variables are developed using Least Square (Gauss-Newton/ Marquardt) steps (Table 4).
For empirical assessment of this relationship, weekly returns of the Abu Dhabi Stock Market General Index (ADXG) and four sectoral indices (Note 3), namely, banking (ADBF), real estate (ADRE), industrial (ADCT), and energy (ADEG) are separately studied in relation to variations in weekly WTI prices for the period between 2012 -29 th week of 2019, i.e., for a period of 392 weeks (out of the 654 weeks shown in Figure 1). These selected 392 weeks cover the 2014 oil crisis and the era of non-oil diversification in the UAE. Most of the recent studies cover GCC economies, however the dimensions and intensity of non-oil diversification in the UAE are different from other GCC countries. Weekly indices data are sourced from the Abu Dhabi Securities exchange (www.adx.ae) and weekly WTI prices per barrel from a reputable online source, namely, investing.com (https://www.investing.com/currencies/wti-usd-historical-data). Data analysis is carried out using EViews software. Tables 2-7 and Appendix A are based on the data sets developed based on weekly WTI oil price data sourced from investing.com and data of various stock indices sourced from Abu Dhabi Stock Exchange.

Vector Error Correction Model
The vector autoregressive (VAR) model is a general framework used to describe the dynamic interrelationship among stationary variables. The vector error correction (VEC) model is just a special case of the VAR for variables that are stationary in their differences (i.e., I(1)). If non-stationary but I(1) time series are cointegrated, the VEC model is applied to examine both short-run and long-run dynamics of the series. The conventional VEC model equation for cointegrated series is: The significant t-statistic on the parameters of ECT indicate existence of the long run relationship and long run causality between the variables. It is a restricted VAR designed for use with nonstationary series which are cointegrated. In the VEC model there are in-built cointegration relations in the specification such that the model restricts the long-run behaviour of the endogenous variables to converge to their cointegrating relationships while allowing for short-run adjustment dynamics. The cointegration term is defined as ECT which relates to the fact that the deviation from long-run equilibrium is corrected gradually through a series of partial short-run adjustments.
ECT is Ordinary Least Square (OLS) residuals from the following long run cointegrating regression: and is defined as - The coefficient of ECT, , is the speed of adjustmentsit measures the speed at which y (return of stock indices) returns to equilibrium after a change in x, i.e., weekly oil price.

Unit Root Test
At first, stationary of variables should be ensured to avoid spurious regression. In this section stationary of variables is checked by applying Augmented Dickey Fuller (ADF), Dickey Fuller GLS (ERS) and  At first difference, null hypothesis is rejected since p value  5% applying ADF, GLS(ERS) and KPSS tests. Test results, presented in Table 2, clearly indicate the presence of a unit root for all the series in levels and a rejection for the series in first-differences, providing evidence of an I(1) behaviour.

Lag Selection
To estimate the Johansen cointegration model, the optimal interval of variables must be provided at first. Thus, LR test and information criterion are used to identify the optimal interval based on "lag length" functionality of Eviews software. Summary of the analysis is presented in Table 3 below, showing the specific rows in which minimum lag has been selected. Based on the result of VAR Lag Order Selection criteria, 2 lags are selected for all series. within -1 and 0. This implies even if there are shocks in the short run, they may affect the movement of the individual series, but would converge in the long run. Based on result of unit root tests, lag selections, and cointegration tests as shown in Sections 3.3-3.5, the application of VEC model appears to be the appropriate choice as a method of data analysis.

Data Analysis
Results of application of VEC model on the five data series are presented in Table 4. Value of C(1) of series are negative and significant. This implies that if there is departure from equilibrium in one direction it would be pulled back. Value of C(1) signifies the speed of correctionit is value of ECT t-1 (Eq.3). ECT should be in negative number , and the positive value means explosive and not reasonable. For example, if the ECT t-1 estimated coefficient is -0.93 (as in the case of Series 1), the estimated coefficient indicates that about 93% of this disequilibrium is corrected within one week since weekly data has been used in this study. This also implies that all explanatory variables Granger causes to explain changes in the indices. The outputs of the VEC model (

Coefficients Diagnostic
Wald test is a way to find out if explanatory variables in a model , in the present study -C(4) and C(5) ( see Table  4), are significant. Their significance here refers to their contributions to the model. And if their contributions are not found to be significant then they can be deleted without affecting the model in any meaningful way. Coefficient C(4) and C(5) are linked by one lag and two lags to LN(OIL) respectively. Thus, the null hypothesis is -

Null Hypothesis C(4) =C(5)=0
For all series, the null hypothesis is rejected since p values are less than 5% for both F-Statistic and Chi-square () Statistic which signify that C(4) ≠ C(5) ≠ 0. Thus, the lag values of the dependent variables are found to be significant in estimating the return of indices.

.2 Residual Diagnostic
The Breusch-Godfrey serial correlation LM test is a test for autocorrelation in the errors in a regression model. The presence of serial correlation would mean that sub-optimal model estimates of parameter have been obtained. Since the VEC models developed (Table 4) for five series include two lag values of LN(OIL) as independent variables, it is necessary to check for serial correlation up to order 'p'. Since this has used two lags, null hypothesis is that 'there is no serial correlation at up to 2 lags'. Table 6 provides the test statics. It is found that null hypothesis of 'no serial correlation' is not rejected with respect to Series 1: LN(ADXG) and LN(OIL), Series 2: LN(ADBF) and LN(OIL) and Series 5: LN(ADRE) and LN(OIL). However, presence of serial correlation is found in cases of Series 3: LN( ADCT) and LN(OIL), and Series 4: LN(ADEG) and LN(OIL). Thus, the VEC model developed for these series may not be a proper fit because of model specification error.

.3 Stability Diagnostic
Stability diagnostic analysis is carried out using recursive estimates (CUSUM Test). The test result is presented in Figure 4. The CUSUM line (marked in blue) falls within 5% significance level reflected by upper and lower boundaries (marked in red). This shows that the specified VEC models of the five series are stable.

Granger Causality Tests
Finally, Granger Causality Tests are carried out to analyze whether one time series , weekly WTI prices in this study, is useful in forecasting another i.e. stock returns and vice versa. In the context of this study, it states that changes in weekly WTI prices "granger causes" (i.e., contain information that helps predicting) weekly return of stock indices in UAE other than lagged value of indices return. Results of Granger Causality Tests of five series are presented in Table 7 which shows that LN(OIL) "granger causes" LN(ADXG), LN (ADBF) , LN(ADCT), LN(ADEG) and LN(ADRE). But stock returns do not Granger cause change in oil price which is consistent with a-priori knowledge.
Accordingly, it is found that returns of stock indices in the UAE are cointegrated with oil price changes. Sectoral indices relating to Banking and Real Estate are also influenced by changes in oil prices. It appears logical as these two industries are primarily driven by oil revenue surplus. However, VEC models with respect to manufacturing and energy sectors, although showing cointegration with change in oil prices and satisfying coefficient diagnostic and stability diagnostic tests, the specified models are subjected to presence of serial correlation and so are not reliable. Further studies are not conducted to identify causes of serial correlation in these two series.  Not Rejected The result of the study signifies that performance of stock market in the UAE is continued to be influenced by oil price volatility. It may be mentioned that proportion of market capitalization of energy sector companies listed on ADX are not substantial. A major portion of the market capitalization is contributed by companies belonging to banking, insurance and financial services. Thus, despite increased contribution of non-oil sector in the GDP, the stock market performance is not decoupled from oil price volatility. This may be because of predominance of oil price linked government revenue. Although contribution of non-oil sectors has increased, the structure of UAE government revenue has not significantly changed. Value added tax and income from other non-oil sources are not significant. Thus, adverse change in oil price would continue to impact the government revenue and consequently government spending for development of non-oil sectors. On the other hand, increased oil price would strengthen budget surplus and improve government spending for the development of non-oil sectors.

Concluding Remarks
The result of this study has important policy implications that along with non-oil diversification of GDP it is equally important to achieve non-oil diversification of government revenue. Perhaps introduction of value added tax as an alternative source of revenue is not sufficient as a means of deriving government revenue from non-oil sector. A recent IMF paper [Olumuyiwa et al (2018)] states MENAP oil exporters are benefitted from subsidy reform, with spending on subsidies reduced while capital expenditure protected, with minimum reduction of one percent of GDP. While tax revenues have only delivered 0.3 percent of GDP in the fiscal balancing process. The UAE performed little better as the VAT collection accounts for about 1.7 per cent of nominal GDP. The IMF paper [20] also highlights that total tax revenue collection in the MENAP region is significantly less than in other emerging market economies. The biggest discrepancy is that non-oil tax revenues represent less than 10 percent of GDP in MENAP oil exporters against more than 20 percent of GDP in emerging market economies. In the UAE, taxation reform including introduction of corporate tax and even low level of personal income tax might change the GDP composition as against the present dependence on fees and stamp duties.
Second, developing non-oil manufacturing sector is difficult because of demographic constraint. The UAE economy is mostly driven of migrant work force. Development of manufacturing sector would necessitate deployment of large migrant work force which impact demographic balance. Thus even taxation reform may have limited impact on decoupling the oil dependency of the economy.
Third, the ADXG is not a broad based index and the sectoral indices have equally narrower base. They get easily influenced by oil price volatility. The stock market indices may not reflect the economic performance of the companies. The narrow investor base of the ADXG also causes a psychological barrier to decoupling from oil shocks. Thus it is important to study impact of oil price volatility on profitability of non-oil sector companies. The impact Saudi market spill -over effect has not been studied in this paper.


s2fieldsofstudy: Economics Business

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Interrelation and Spillover Effects Between Stocks and Bonds: Cross-Market and Cross-Asset Evidence

This paper examines the behaviour of stock and bond markets across four major international countries. The results confirm the view that same asset-cross country return correlations and spillovers increase over time. However, the same in not true with variance and covariance behaviour. Volatility spillovers across countries exhibit a substantial amount of time-variation, however, there is no evidence of trending in any direction. Equally, cross asset-same country correlations exhibit both negative and positive values. Further, we report an inverse relation between same asset-cross country return correlations and cross asset-same country return correlations i.e., the stock return correlation across countries increases at the same time the stock and bond return correlation within each country declines. Moreover, results show that the stock and bond return correlations exhibit commonality across countries. Results also demonstrate that stock returns lead movement in bond returns, while US stock and bond returns have predictive power other country stock and bond returns. In terms of the markets analysed, Japan exhibit a distinct nature compared with those of Germany, the UK and the US. The results presented here provide a detailed characterisation of how asset interact both with each other and cross countries and should be of interest to portfolio managers, policy-makers and those interested in modelling cross market behaviour.

variance approach to examine volatility spillovers between Euro exchange rate series. Diebold and Yilmaz (2009,2012) introduce the spillover index methodology, which utilises a VAR framework to examine the time-varying nature of spillovers and provides an overall measure of spillover strength.
Examining the correlation across markets for the same asset and across assets occupies a large area of research given its importance in portfolio building and diversification. The literature has reached a broad consensus that correlations for the same asset have trended upwards over time due to increased financial integration (although a debate surrounds the potential for contagion effects to impact correlation behaviour, see for example, Forbes and Rigobon, 2002;Bekaert et al, 2005;Dimitriou et al, 2013). However, a much larger debate exists about the nature of correlations across asset classes. With reference to the correlation between stocks and bonds, there is evidence of significant time-variation and cycling between periods of both positive and negative correlations. For example, the expectation of a positive correlation between stock and bond returns is identified by, among others, Barsky (1989), Shiller and Beltratti (1992) and Campbell and Ammer (1993). However, a negative correlation that may arise during times of economic stress and result from a flight-to-safety effect, is highlighted by, for example, Gulko (2002), Connolly et al. (2005) and Andersson et al (2008). Baur and Lucey (2009) also consider the role of contagion as well as flight-to-safety effects in the nature of the stock and bond relation, while Kim et al (2006) argue that segmentation between of bond and stock markets leads to a falling correlation. McMillan (2019) also notes changing correlations between assets linked to economic conditions. Both Connolly et al (2007) and Baur (2010) examine the potential interaction for same asset and cross-asset correlation. Notably, the latter argues that higher risk leads to rising same asset correlation through a contagion effect and falling cross-asset correlation due to flight-to-safety.
Understanding the interaction between stock and bond returns is a key ingredient in the construction of portfolios. Stocks and bonds still form the majority of asset holdings within portfolios and the time-varying nature of the correlation has implications for diversification benefits. Moreover, any temporal interaction between the two assets will also benefit investors in timing changes in asset allocation. Tolikas (2018) examines the lead and lag relation between stocks and bonds and argues that while the former exhibits no such leading role for investment grade bonds, it does so for high yield (and higher risk) bonds. Extending this line of research further, spillovers in the correlation between stocks and bonds across markets may indicate that investor risk appetites are changing globally, as switching between stocks and bonds in one market, affects similar holdings in another market. 1 A key issue that arises is how to construct both volatility and correlation series and examine their interaction. This arises as neither of these series are observable. A common approach to generating volatility series is the GARCH methodology (Engle, 1982;Bollerslev, 1986), although using squared returns is not uncommon (see the general discussion in Pagan and Schwert, 1990, and as an example of its use, McMillan et al, 2000). For the correlation, an obvious approach is to use an extension of the GARCH model that allows for the joint modelling of asset returns and their covariance. Examples of this include, Baur and Lucey (2010) who use a multivariate-GARCH model and Colacito et al (2009), who use an extension of the DCC model of Engle (2002). An alternative, simpler, approach is to use rolling windows for the correlation between two series. Fan and Mitchell (2017) use a 1-year and 5-year rolling window to illustrate the nature of time-variation, while Rankin and Shah Idil (2014) consider a variety of window lengths. A more recent approach builds upon the realised volatility literature (see, McAleer and Medeiros, 2008 for a general review). Using this approach, we can 1 An examination of the interaction between stocks and bonds can also be considered through the bond beta, which examines the riskiness of bonds and is constructed as the covariance between stock and bond returns divided by the variance of stock returns (i.e., the equivalent of a CAPM beta). This measure, thus, captures systematic risk in bonds and we can examine whether such risk transmits across markets. Existing work examining the behaviour of the bond beta includes Viceira (2012), Campbell et al (2017 and Aslanidis et al (2019). construct realised measures for both volatility and covariance and thus construct the realised correlation. This approach is taken by Aslanidis and Christiansen (2012) for the stock and bond correlation. Evans and McMillan (2009) consider both a GARCH and realised correlation approach to examine co-movements across a wide range of international stock markets. This paper seeks to examine the interactions between stock and bond markets across four major countries and financial centres (Germany, Japan, the UK and the US) and tie together different literatures that consider correlations and causality (spillovers) across assets and markets. Specifically, in this paper we consider the spillover and causality effects between international stock and bond markets, including both within and across countries. The paper also considers the time-varying nature of correlations both for the same asset across countries and across assets. Thus, the paper seeks to provide a complete characterisation of the nature of the interrelations between stocks and bonds across major international markets. The results in this paper should be of interest to investors, academic and policy-makers, as they will aid our understanding of how assets interact with each other and across markets. We focus on monthly observed interactions as this is relevant for both portfolio managers and policy-makers for whom temporary high-frequency movements will carry less information in comparison to more persistent lower frequency changes. This will improve our knowledge of how information flows across assets and markets allowing investors to improve portfolio building and policymakers to engage in any necessary corrective action.

Empirical Methodology.
The empirical method used in this study focusses on the vector autoregression (VAR; Sims, 1980) and two related techniques, Granger causality tests and the spillover index of Diebold and Yilmaz (2009,2012). The general k-variable, p-lagged VAR model is given by: (1) xt = ∑i=1 p φi xt-i + εt where xt represents the vector of k endogenous variables, while φ is a kxk matrix of parameters for each time lag, p, and εt ∼ (0,Σ) is a vector of disturbances that are assumed to be independently and identically distributed over time. To determine the lag length of the VAR, we use the AIC, which should ensure white noise residuals.
To examine Granger (1969) causality, we can specify a two-variable VAR as such: (2) 1 = ( ) 1 + ( ) 2, + 1, where P(L), Q(L), R(L) and S(L) are one-sided lag polynomials of order p, q, r and s. The regression errors are assumed to be mutually independent and white noise. The null hypothesis that x2 does not Granger-cause x1 is rejected if the coefficients on the elements in Q(L) are jointly significantly different from zero. Bi-directional causality exits if the coefficients in both Q(L) and R(L) are jointly significantly different from zero.
To examine the nature of spillovers between series, we use the approach of Diebold andYilmaz (2009, 2012) and, in particular, the generalised VAR framework of Koop et al (1996) and Pesaran and Shin (1998) implemented in Diebold and Yilmaz (2012). This approach allows the variance decomposition to be invariant to the ordering of the VAR variables.
Assuming covariance stationarity, equation (1) can be rewritten as an infinite moving average model, as such: The parameter matrices, Ai, are recursively defined as follows: A1 = φ1 Ai-1 + φ2 Ai-2 +… + φp Ai-p and with A0 a kxk identity matrix. The variance decompositions allow the fraction of the H-step ahead error variance in forecasting xi owing to shocks arising from xj, where i≠j to be calculated. The H-step-ahead forecast error variance decomposition is given by: where Σ is the (estimated) variance matrix of the error vector ε, σii the (estimated) standard deviation of the error term for variable i, and ei is the selection vector with one as the ith element and zero otherwise.
Each element of the variance decomposition matrix is then normalised by the sum of the elements of each row of the decomposition as such: This is to ensure that the own and cross-variable variance contribution sum to one under the  by construction. The total spillover index is then defined as: A key issue in the analysis is to calculate the variance and covariance across series, as such variables are typically unobserved. One common approach is the GARCH methodology, including the DCC model, to obtain fitted values for the variance and correlation. However, a drawback of this general approach is that there is no preferred model specification and the resulting series are subject to estimation error. To calculate the variance and covariance/correlation, we use the realised volatility approach, which utilises higher frequency data to compute the lower frequency variable of interest. This approach has the advantage of reducing noise within the constructed series, allowing for more accurate estimation, while the series can be treated as observed and modelled directly. The realised volatility approach largely began with Andersen and Bollerslev (1998), although its use pre-dates that, with French et al (1987) and Schwert (1989) both using daily data to construct monthly volatility. Since the work by Andersen and Bollerslev (1998), the use of higher frequency data in constructing lower frequency variables has become popular (see, for example, Andersen et al, 2003;McAleer andMedeiros, 2008, Nakajima, 2019). Realised volatility is constructed by summing over the lower frequency, the squared returns of the higher frequency data. Thus, we obtain daily returns data, which is squared and summed over the month, which is the frequency of interest. Likewise, the realised covariance between two assets, e.g., stock and bond returns, is obtained as the product of the two asset returns. Respectively, two series are generated as: where, d refers to the number of days in a month, M. The realised variance in equation (7) is constructed for both the stock and bond return series, where i=s and b. The realised correlation, ρ, series is then constructed as: (9) , = , / (√ , 2 √ , 2 ).

Data.
We obtain stock and bond return data from DataStream for Germany, Japan, the UK and the US. The data is obtained daily over the time period from the first day of 1980 (with the exception of Japanese bond data, which is only available from the first day of 1984) to the last day of May 2018. The index data is based on the Datastream total market index for stocks and the government (Treasury) 10-year constant maturity index for bonds. 3 As our modelling frequency is monthly, we use the daily data to construct monthly returns, volatility, covariances and correlations. 4 Monthly returns are calculated as the first-difference of the log of the end of month price. For the volatility and correlation series, as outlined above, we use the realised variation approach. Thus, we obtain squared daily returns and aggregate these over the month to form the volatility series. The monthly realised covariance is the sum over the month of the daily cross-products of the returns series. Monthly correlations are then calculated as the covariance series divided by the product of the two corresponding standard deviations. Noticeably lower volatility can be observed during the early 1980s, early 1990s and the latter 2010s. Across the four markets, we can observe that comparatively Japan exhibits higher volatility across the sample. For the bond market, we generally see higher volatility at the beginning of the sample when interest rates across these markets were typically around the 10% mark. Subsequently, as interest rates fell, so did bond market volatility, until the financial crisis, whereupon volatility rises before falling back in the latter 2010s. We also present the usual summary statistics in Table 1, which are consistent with established stylised facts.

Correlations Across Assets and Markets
Before examining the nature of Granger causality and spillovers between the stock and bond series across the four markets, we briefly consider the nature of correlations across markets and assets. Figure 2 presents the same asset correlations between bond and stock returns across the four countries. As noted in the Introduction (e.g., Kim et al, 2006;Connolly et al, 2007;Baur, 2010), previous evidence points to a rising correlation between the same asset across international markets. For the interactions between Germany, the UK and the US, we see this trend continuing with the strength of the correlation increasing, particularly from the 1990s onwards. Of further interest, we observe the rise in correlation plateauing, and even falling, towards the end of the sample. In contrast, for Japan, the general pattern of the stock and bond return correlations is one fluctuating around a constant mean value. Figure 3 presents the plots of the stock and bond correlations for the four markets.
Across the four markets, we can observe that while the stock and bond return correlations exhibit a relatively high degree of variability, there is a noticeable decrease occurring from the late 1990s and, more obviously, in the early 2000s. Subsequently, the correlation rises in the mid-2000, falls again in the latter 2000s and then begins to rise around the mid-2010s. The periods of falling correlations are consistent with those of stock market stress, such as the dotcom crash and financial crisis, which supports flight-to-safety behaviour with investors moving out of equities and into bonds. The higher correlations are thus, more associated with normal periods of market behaviour. We can also observe a higher degree of similarity in the correlations for Germany, the UK and the US, while those for Japan indicate different behaviour. For example, the correlation across the stock and bond correlation series between Germany, the UK and the US is over 0.8, while it is less than 0.5 for Japan. Baur (2010) links the behaviour between the same asset across markets and different assets within the same market. Baur argues that a rise in the correlation of the same asset across international markets is consistent with a fall in the correlation across assets within the same international market. Notably, a period of market stress can lead a contagion effect between international stock markets raising their correlation, while a flight-to-safety effect from stocks to bonds lowers their correlation. This joint contagion and flight-to-safety argument would imply similar behaviour in the stock and bond correlation across markets as investors in each country act in the same way, selling risky stocks and buying safer bonds. From Figure 3, we do observe similarity in the stock and bond correlations across the four markets.
To further consider the idea that same asset-cross market and cross asset-same market correlations move in different directions due to the joint contagion and flight-to-safety effect, we can examine their interactions. Table 2 presents the correlation between same asset-cross market and cross asset-same market correlations. For example, any given entry is the correlation between the stock and bond correlation in a country with the stock-stock or bondbond correlation between pairs of countries. From these correlations we can consider the view that a stronger correlation between the same asset (contagion) occurs at the same time as a weaker correlation across assets (flight-to-safety).
The results from this exercise broadly support the above view and again present a distinction between the results that include Japan. Considering the results across each row, we can see whether the stock and bond correlation for each market is related to the same asset correlation across markets. Examining the results for the stock and bond correlation for Germany, the UK and the US, we can see there is a strong negative relation with the corresponding markets bond and stock correlation across other markets. For example, the German stock and bond correlation exhibits a correlation with the German and UK or US bond and stock returns correlation of over (in absolute terms) 0.50. To be more specific, the correlations between the German stock and bond correlation and the German and UK bond return correlation is -0.629, while it is -0.541 with the German and UK stock return correlation.
Hence, a large negative relation between the same asset-cross market and cross asset-same market correlations. Similarly, strong results are reported for the UK and US stock and bond correlations with international same asset interrelations. These values all support the view that a stronger same asset correlation is consistent with a weaker cross-asset correlation. As before, the results for Japan differ, with very limited evidence of any relation between the same and cross asset correlations.
The results in this section suggest two important conclusions that are of relevance to investors, policy-makers and those engaged in modelling market behaviour. First, the dynamics of correlations across assets and markets differ when they involve Japan compared to the other major markets. Second, there is an identifiable relation between cross asset-same market and same asset-cross market relations. When the cross asset-same market correlation rises, the same asset-cross market correlation falls.

Mean and Variance Causality and Spillovers Within Assets
To examine mean and variance spillovers, a separate VAR model is estimated for the mean and variance series across the four countries. In each case the VAR lag lengths are determined by the AIC and are two and one for the stock and bonds returns respectively, and two and nine for the stock and bond variance series respectively. 5 In order to present the results in a manageable fashion, Table 3 reports the results of the Granger causality tests for stock market returns and variance using the estimated VARs, for which we report the associated F-statistic and p-value. For bond returns (Table 4), we find evidence of bi-directional causality between Germany and Japan and between Japan and the UK. There is also evidence of causality running from US bond returns to both German and Japanese returns. For bond variance, we see bidirectional causality between Germany and Japan, Japan and the UK, Japan and the US and the UK and US.
Across both tables, we can see greater evidence of causality in the bond market compared to the stock market. At the 5% statistical significance level, there are four and five significant relations for stock returns and variance respectively, while for the bond market the equivalent figures are six and nine. For the stock market, both returns and variance, we observe that predominately the direction of causality is from the UK and US towards Germany and Japan, while for the UK and US, the latter directs causality to the former in returns and receives in variance. Germany and Japan, which predominantly are recipients of causality exhibit no relation with each other. For the bond market, in contrast, Germany and Japan exhibit bidirectional causality and there is greater interaction between Japan, the UK and the US across both returns and variance. These results illustrate the view that major stock market information emanates largely from the US and then the UK, while bond market information arises across each of the major global financial centres.
To further examine the nature of the relations between stock and bond returns and variance across the four markets, we use the spillover index approach of Diebold and Yilmaz (2009,2012). We only report the time-varying spillover graphs, in Figure 4, while the remaining information (variance decompositions) is available upon request but provides similar information to the Granger causality results. The stock return spillovers graph reveals that spillovers are increasing over the sample period at a relatively steady rate but with a noticeable upward jump for the financial crisis and with a shallower trend afterwards.
Specifically, the spillover index increased from around 40% to 50% from the mid-1990s until 2007, whereupon (after a small drop) it increased to 58% by the start of 2009, after which it continued to increase to 62%. The spillover index for bond returns also increases over the sample period. However, prior to crisis, the index fluctuated around a constant mean in the low 40%. Again, we see a jump associated with the crisis, from about 42% to about 47%, after which the spillover index has trended to almost 56% by the end of the sample. Thus, the behaviour of these return spillovers largely mimics the movements in the equivalent return correlations, trending upwards over time.
The spillover index plots for the variance series reveal a different pattern compared to the return series, but again have similarities across stock and bond variance. For both variance series, the value of the spillover index at the start and end of the sample is broadly similar. For stock variance, the value of the spillover is approximately 64% at the start of the sample, this falls to around 50% in 2004 as stocks recover from the dotcom crash but then jumps to around 72% during the financial crisis before settling and remaining at around 67% until the end of the sample. For bond variance, the value of the spillover index is around 41% at the start of the sample, falls to 30% during the early 2000s as interest rates fall in response to the dotcom crash before recovering during the rest of the 2000s, with a noticeable jump for the financial crisis.
By the end of the sample, the spillover index is back to around 41%. Thus, while return spillovers have increased through the sample period, variance spillovers, although exhibiting substantial fluctuation, remain relatively constant.

Mean and Variance Causality and Spillovers Across Assets
In the previous section we examine the nature of spillovers between the return and volatility of stocks and bonds separately across the four markets, i.e., the behaviour of the same asset across international markets. In this section, we consider the behaviour across assets within the same international market. Specifically, we examine the nature of the interrelations and spillovers between stocks and bonds within each of the four countries we examine. An examination of the underlying VAR reveals that in each case, the coefficient sign on the significant lagged stock return series in the bond return equation is negative. Thus, a rise in the stock return corresponds to a fall in the bond return in the subsequent month, and equally a falling stock return leads to a rising bond return. This accords with the view that stocks and bonds are competing assets and investors move between them as their risk appetite changes.
This result differs from that of Tolikas (2018) who argues the any leading relation from stock to bonds returns only exists for speculative bonds and not investment grade bonds. Our results may differ as we consider sovereign bonds, whereas Tolikas only examines corporate bonds.
As with the above same asset, cross-country results, we present the spillover index in Figure 5. Across all countries, we can see that spillovers were higher during the late 1990s and early 2000s when the dotcom bubble reached its peak and then crashed. This higher spillover indicates that investors were moving between stocks and bonds over this period. Spillovers fell as stocks began to recover during the mid-2000s, but again rose during the financial crisis and remained relatively higher. 7 That said, we note, the behaviour of Japanese stock and bond spillovers differ from those of the remaining markets.
Given the results of the above analysis, we further examine the predictive effects between stock and bond returns. Specifically, the results in Table 3 reveal Granger causality across international stock and bond markets, while the results in Table 5 reveal Granger causality across stock and bonds within each market. Notably, Table 3 indicates causality running from the US stock market to each of the other markets, while Table 5 indicates causality from stocks to bonds. Table 6, therefore, presents the results of a standard single equation predictive regression model for the stock and bond return in each market, regressed on a lag of the home market stock and bond return and the stock and bond return from the US.
As home and US stock and bond returns respectively are likely to be highly correlated and thus encounter a multicollinearity problem, we orthogonalize home market returns. Here, we estimate a regression of home market returns on contemporaneous US market returns and obtain the residual. This residual thus captures home market information that is adjusted for (orthogonal to) US information and this approach follows that in Stehle (1977), McMillan (2016) and Lawrenz and Zorn (2018).
These results reveal an interesting role for US market information across international stock and bond markets. If we consider the bond return regressions for Germany, Japan and the UK, we note that the results in Table 5 indicate that the stock returns of these markets Granger cause the bond returns.

Causality and Spillovers in Stock and Bond Relations Across Markets
The previous section considers how stocks and bonds interact in terms of their lead/lag relation and the nature of spillovers and causality. The correlation between stocks and bonds plays a critical role in portfolio management, as investors will move towards one particular asset given changes in their preference or perception of risk. While, we consider the general pattern in the stock and bond correlation above, here, we examine whether the correlation in one market also spillovers to other markets.
As with the mean and variance series we estimate a VAR model for the contemporaneous stock and bond return correlations and consider both the Granger causality test and Diebold and Yilmaz spillover index. 8 Table 7 reports the Granger causality test between the stock and bond return correlations across the international markets, where the lag length in the VAR is five. The results suggest bidirectional causality across the correlations for Germany, the UK and US. In contrast, at the 5% significance level, there is no causal relation involving Japan, although there is marginal evidence running from Japan to Germany. Where the correlation represents investors holdings of stocks and bonds, these results suggest commonality in the behaviour of investors across international markets, except for Japan.
To support the Granger causality results, Figure 6 presents the time-varying spillover index. Here, we can see that over the first part of the sample, which covers part of the dotcom crash, the spillover index rises from about 36% to a value in the low 40%s by the mid-2000s as the stock market began to recover from the crash. From this point, the index remains broadly flat, fluctuating around a relatively constant value with only a small rise to the mid-40% range following the financial crisis period.

Discussion
The above analysis presents a series of results that can aid our understanding of the movement between the same asset across countries, different assets within a country and different assets across countries. This will improve our knowledge of market interactions, including the transmission of information across both assets and markets. This may be of use to those engaged in portfolio building, policy-making and developing models of market behaviour.
Our results reveal that correlations for the same asset across international markets rise over time, while the correlations for different assets within the same market exhibit substantial variation and both rising and falling periods and negative correlations prominent after 2000.
Results also support an emerging view (see, Baur, 2010)   . Examining the co-movement (correlation) between stocks and bonds across international markets, we observe a separation in behaviour. The stock and bond correlations show evidence of bi-directional causality and spillover across Germany, the UK and the US, however, movements in Japan appear unrelated. Indeed, the different behaviour of Japan is a consistent theme in the results presented here, not only differing in the correlation spillovers but also in stock return and volatility spillovers as well as the dynamics of the within market stock and bond return relation. The segmentation of Japanese financial markets has been a recurring theme in previous research and is reported by Arshanapalli and Doukas (1993), Berben and Jansen (2005) and Morana and Beltratti (2008).
These results support a particular direction of information flow across international markets and assets. For returns, we see a pattern of information flows emanating from the US to the other markets (a similar result is reported by Ehrmann et al, 2011, in respect of Euro markets). US stock returns affect US bond returns, while both affect international stock and bond returns. For variance (and notably bond return variance), we observe greater evidence of information flows being transmitted across the different international financial centres. For the stock and bond return correlation, we see interaction across the German, UK and US markets but with the Japanese market appearing more isolated. Regarding the strength of these spillover effects, the spillover index for stock and bond returns continually increases over the sample period. However, the same is not observed for the variance and covariance behaviour. The variance spillovers, while exhibiting notable movements around crisis periods, are broadly the same at the start and end of the sample period. The correlation spillover index rose in the early 2000s but then remained broadly flat after the mid-2000s. This implies crucial distinctions in how different aspects of information are transmitted across markets, while return spillovers appear to continually strengthen, how investors move between stocks and bonds in one market exhibits less spillover behaviour, with local information retaining its importance.
The results supporting the pre-eminent role of US stock returns in having a conditioning effect on the stock and bond returns of other markets, extends the results of Rapach et al (2013).
They demonstrate that US stock returns play a key role in predicting movements of stock returns in a range of international markets, we show that this is equally true of bond markets.
These results also extend the work of Tolikas (2018) who notes a predictive relation from stocks to speculative bonds within individual countries. Our results here support a predictive effect of stocks to sovereign bonds across countries.
The spillover index results further support the view that stock and bond return movements across markets continue to rise in strength. The rise in the interconnection of stock returns has been well documented (e.g., Longin and Solnik, 1995;Forbes and Rigobon, 2002;Kotkatvuori-Örnberg et al, 2013;Evans et al, 2017). In contrast, for volatility, while such spillovers exhibit a large degree of movements, their strength has generally remained constant.
A similar result is reported by Tiwari et al (2018) for four different asset classes.
Moreover, in extending these lines of research, we demonstrate the interactions across markets in the nature of the stock and bond correlation. This has previously not been examined and here we observe two distinct phenomenon. The stock and bond interaction in the markets of Germany, the UK and US are related and show evidence of bi-directional causality. This supports the view of commonality in investor decisions regarding stock and bond holdings in their portfolios across these markets. Whereas the stock and bond covariance for Japan exhibits no such commonality. Further, the strength of this interaction, measured through the spillover index, exhibits periods of both strengthening spillovers, notably over the first half of the 2000s, and weakening spillover, during the 2010s. Thus, while there is evidence of rising spillovers between the individual assets, this does not equally hold for portfolios of assets.

Summary and Conclusion.
This paper examines stock and bond returns, volatility and realised correlation for Germany, Japan, the UK and US, and investigates the nature of correlations and, through VAR models, Granger causality and time-varying spillovers. Thus, we provide a complete characterisation of mean, variance and covariance behaviour across these markets. Understanding the interaction between markets (both geographic and asset) and the transmission of information, is important for portfolio managers, policy-makers and academics.
The results suggest several key findings, some of which serve to reinforce our existing knowledge, while others add to our body of understanding. In confirmation and extension of previous work, we observe that return correlation and spillovers for the same asset across countries exhibits upward trending behaviour. The equivalent spillover results for volatility indicate a large degree of time-variation but with no given direction. We also support previous results in which US stock returns exhibit leading behaviour for other international stock returns.
We further expand this result to include the behaviour of bond returns, with US bond returns exhibiting predictive content for German and Japanese bond returns. Moreover, bond markets show a greater degree of interaction across markets for return and volatility behaviour, whereas stock markets exhibit greater directional flows. Further, a key result is that stock returns consistently lead (predict) movements in bond returns. Our results also support an interesting pattern of behaviour in which same asset-cross market and cross asset-same market correlations move in opposite directions. This suggests a joint contagion and flight-to-safety effect.
In addition to examining stock and bond returns and volatility across and within international markets, we also look at the correlation behaviour between stocks and bond across markets. Here, two interesting results emerge. First, whereas the correlation and spillovers between stock and bond returns across different markets rise over time, the same is not true with the correlation. Cross market behaviour of the stock and bond return relation strengthens in the early 2000s and then plateaus from the late 2000s. Thus, while stock returns exhibit strengthening relations, this pattern is not replicated for variances and covariances. Second, there is evidence of interrelations and bidirectional causality between the markets of Germany, the UK and the US, whereas Japan appears distinct, a result also noted with stock return behaviour.
In sum, we provide evidence that stock returns exhibit predict content for bond returns, that US stock returns contain predictive power for all market stock and bond returns, that there is commonality in the moment of stock and bond return covariances across the markets of Germany, the UK and the US, but Japan appears less integrated and while stock returns continue to exhibit greater integration the same is not true of stock and bond market variances and covariances. The results here should allow investors to improve portfolio decision-making, policy-makers to understand (and mitigate) how information flows across markets and aid those engaged in seeking to model market and investor behaviour.  Entries are the correlation coefficient between the stock and bond return correlation for each individual country, given in the first column, with the same asset correlation across two countries, given in the second row. As an example, in the first cell 0.015 is the correlation coefficient between the correlation between German stock and bond returns with the correlation between German and Japanese bond returns.   (and associated p-value) for the null hypothesis of no Granger causality in a VAR whose lag length is determined by the AIC.  (and associated p-value) for the null hypothesis of no Granger causality in a VAR whose lag length is determined by the AIC.  (and Newey-West t-values) of the predictive regression of each countries stock and bond return regressed on a lag of their own returns and a lag of the US returns (the home and US returns are orthogonalised prior to estimating the above model).