A spatial analysis of international stock market linkages

Transcription

1 A spatial analysis of international stock market linkages Hossein Asgharian, Wolfgang Hess and Lu Liu * Department of Economics, Lund University Box 7082, S Lund, Sweden. Work in progress Abstract The severe global impacts of the recent financial crises have intensified the need to understand how country specific shocks are transmitted to other countries. Using spatial econometrics techniques, we analyze to what extent various linkages between countries affect the interdependence of their stock markets. We analyze a number of different linkages: geographical neighborhood, similarity in industrial structure, economic integration (measured by the degree of countries bilateral trade and bilateral foreign direct investment) and monetary integration (measured by the closeness of countries inflation rates and the stability of their bilateral exchange rate). We analyze both return and return volatility of country indexes for a large sample of 41 countries over a period of 16 years. Our empirical results indicate that economic factors affect the dependencies among financial markets to a greater extent than geographical neighborhood or monetary integration. In particular, we find that a country s market return and volatility depend to a large degree on market returns and volatilities in countries that are similar in industrial structure and those that are important trading partners. By identifying several linkages through which stock markets are connected with each other and assessing the relative importance of these linkages, we provide new insights which can be used by financial investors for risk hedging through global diversification. * Tel.: ; fax: address: Hossein.Asgharian@nek.lu.se; Wolfgang.Hess@nek.lu.se; Lu.Liu@nek.lu.se We are very grateful to Jan Wallanders och Tom Hedelius stiftelse and Bankforskningsinstitut for funding this research.

2 1. Introduction The severe global economic impacts of the recent financial crises have intensified the needs for modeling linkages between different financial markets. It is important for financial investors to understand how country (market) specific shocks are transmitted to other countries (markets), because it affects their ability of risk hedging through global diversification. Interactions among international stock markets have been studied by a number of earlier studies. Some studies, e.g. Erb et al. (1994), Longin and Solnik (1995), and Karolyi and Stulz (1996), have focused on correlations between stock market returns, while others, e.g. Bekaert and Harvey (1995, 1997), Bekaert et al. (2005), Asgharian and Bengtsson (2006) and Asgharian and Nossman (2011), have addressed the issue of risk spillover across markets. The majority of previous studies have solely focused on assessing the degree of dependence among markets, whereas the channels through which stock markets are related to each other have usually been ignored. Exploring the underlying economic structures which affect the co-movements of financial markets helps us to properly assess the sensitivity of the markets to exogenous shocks. The recent developments in spatial econometrics provide appropriate tools for analyzing this subject. Applying spatial econometrics makes it possible to incorporate factors related to location and distance in the analysis. Using this approach, the structure of the relationship between observations at different locations will be connected to the relative position of the observations in a hypothetical space, for example the geographical location of a country. We employ these tools to investigate which attributes affect the

3 transmission of shocks among different markets. Our aim is to identify to what extent different linkages between markets affect the degree of market co-movements. We use different attributes to map the spatial location (distance/closeness) of financial markets and analyze the degree of spatial dependence among them. The existence of spatial dependence can be motivated by two different concepts, one that relies on omitted explanatory variables and a second that is based on spatial spillovers stemming from contagion effects (see e.g. LeSage and Pace (2009)). Our study focuses on the latter concept. We analyze a number of different linkages: geographical neighborhood, similarity in industrial structure, economic integration (measured by the degree of countries bilateral trade and bilateral foreign direct investment) and monetary integration (measured by the closeness of countries inflation rates and the stability of their bilateral exchange rate). We analyze both return and return volatility of country indexes for a large sample of 41 countries over a period of 16 years. Our empirical results indicate that economic factors affect the dependencies among financial markets to a greater extent than geographical neighborhood or monetary integration. In particular, we find that a country s market return and volatility depend to a large degree on market returns and volatilities in countries that are similar in industrial structure and those that are important trading partners. To our knowledge this is the first in-depth analysis of the underlying economic structure of global stock market interactions. By identifying several linkages through which stock markets are connected with each other and assessing the relative importance of these

4 linkages, we provide new insights which can be used by financial investors for risk hedging through global diversification. A critical issue in risk management is to obtain a precise estimate of the future correlation between markets. The estimate is sensitive to the choice of methods and the length of the estimation sample. Our results can be used as additional information to improve correlation prediction when making investment decisions. The remainder of the paper is organized as follows. Section 2 presents the spatial econometrics methods used in this paper. Section 3 describes the data sources and the model specifications used the empirical analysis. Section 4 contains the empirical results, and Section 5 concludes the paper. 2. Econometric Modeling The concept of spatial dependence in regression models reflects a situation where values of the dependent variable at one location depend on the values of neighboring observations at nearby locations. Such dependencies can originate from e.g. spatial spillovers stemming from contagion effects or from unobserved heterogeneity caused by omitted explanatory variables. Depending on the source of the spatial correlation, a variety of alternative spatial regression structures can arise. The two most commonly applied spatial regression models are the spatial autoregressive (SAR) model and the spatial error model. The latter models spatial dependence in the disturbances and the former tackles the problem of spatial correlation by including linear combinations of the dependent variable (so-called spatial lags) as additional regressors. One fundamental limitation of spatial error models is that these models rule out spillover effects by

5 construction (see e.g. LeSage and Pace, 2009). Since risk spillovers have an important effect on the dependencies among financial markets, our empirical analysis relies solely on the SAR model. 1 Formally, we consider the following SAR specification with two spatial lags:, (1) where and are spatial autoregressive parameters, and and are (possibly time-varying) spatial weights matrices describing the spatial arrangement of the cross section units. The dimension of and is N N, where N is the number of crosssectional observations in the sample. The model specification above is expressed in stacked matrix form. The vector contains NT observations of the dependent variable (monthly volatility or monthly return), where T is the time-series dimension. Similarly, is a NT k-matrix containing the stacked observations on k explanatory variables (including individual-specific intercepts) and is the corresponding k 1-vector of parameters. Finally, is an NT 1-vector of idiosyncratic error terms, is an identity matrix of dimension T, and denotes the Kronecker product. The distinctive feature of the SAR model is that it contains linear combinations of the dependent variable as additional explanatory variables. This induces an endogeneity problem which renders conventional OLS estimates of the model parameters inconsistent. Maximum likelihood estimation can be used as an alternative to OLS that yields 1 Anselin (1988) also provides a persuasive argument that the focus of spatial econometrics should be on modeling the effects of spillovers.

6 consistent parameter estimates. The log-likelihood function that is to be maximized is given by Where ln L ln ln 2 (2) and is the error variance that is to be estimated along with the structural model parameters (see e.g. Anselin, 2006). Maximizing the likelihood function above is not equivalent to minimizing the sum of squares as in the conventional linear regression model. The crucial difference is the presence of the log-jacobian terms ln. This illustrates why OLS does not yield consistent estimates of the SAR model parameters. The log-jacobian terms also impose constraints on the parameter space for and, which must be such that 0. Since this study focuses on the identification of linkages through which shocks are transmitted across markets, the specification of and is of crucial importance. In our empirical analysis we have defined these matrices in a way that allows for asymmetric dependencies between any pair of markets. In specifying and we start out with constructing a Boolean contiguity matrix that indicates for any pair of markets in the sample whether market is a neighbor to market according to various

7 definitions of neighborhood. 2 The element in the th row and the th column of takes on the value one if market is contiguous to market, and zero otherwise. For each market, the 50% of remaining markets that are closest according to the respective definition of neighborhood are considered to be neighbors. Similarly, we construct a Boolean matrix with individual elements equal to one if market is not a neighbor to market. Formally, this matrix is computed as, where is an N N-matrix of ones and is an identity matrix of dimension N. The spatial weights matrices and are then obtained by row-standardization of and, respectively. Using an SAR(2) model with spatial weights matrices as defined above has two noteworthy implications. First, this model specification allows us to directly compare the spatial dependencies existing among neighbors with those existing among non-neighbors. Second, our specification of and allows for asymmetric dependencies between any pair of markets. For example, when defining neighborhood based on the amount of bilateral trade, the U.S. are contiguous to the Philippines, since the volume of trade between the Philippines and the U.S. is above the median volume of trade between the Philippines and all other countries. The Philippines, however, are not a first-order neighbor to the U.S., since their bilateral trade is below the median volume of trade between the U.S. and all other countries. Although the focus of this study is on spatial dependencies among markets, we also account for spatial heterogeneity among markets by including a number of fundamental 2 The various definitions of neighborhood are explained in detail in Section 3.

8 explanatory variables, which may affect market returns and volatilities, in the model. A number of researchers have noted that SAR models require special interpretation of the -parameters associated with these explanatory variables (see e.g. Anselin and LeGallo, 2006, or Kelejian et al., 2006). In essence, is no longer equivalent to the marginal effects of changes in the fundamentals. The reason for this is that a change in fundamentals in one country, say country i, affects the volatility of that country, which in turn affects the volatilities at nearby locations, which then feed back to the volatility of country i. The values of should thus be interpreted as average immediate effects of changes in the explanatory variables, which do not include such spill-over and feedback effects. 3. Methodology and Data This section describes the selected channels of spatial dependence, i.e. financial integration, economic integration and geographical closeness. For each channel, we define spatial distances among markets and hence the contiguity matrix. In addition, we present the selected control variables included in the model. We also make prior predictions on their signs of impact on market returns and volatility. The remained part of this section describes data sources Potential channels of spatial dependence We use three types of bilateral factors capturing the relative distance/closeness of the financial markets to one another, in order to investigate the determinants of the degree of dependence among different markets. The first type defines financial integration, among them: exchange rate volatility, absolute difference between inflations. The second type

9 captures economic linkages (e.g. bilateral trade, bilateral foreign direct investment and similarity of industrial structure). The third type is distance between capital cities, which describes geographical distance Financial factors Exchange rate volatility An environment with stable exchange rates should reduce cross-currency risk premiums and imply more similar discount rates. This should give a more homogenous valuation of equities and increase incentives to invest in foreign markets. Hence a less volatile exchange rate is expected to increase the degree of dependence. (see for example Bekaert and Harvey (1995) and Baele (2005)). We estimate exchange rate volatility as standard deviation of daily bilateral exchange rates in each month. Absolute difference between expected inflations Absolute difference between expected inflation of two countries measures the degree of monetary integration across the countries. Convergence of expected inflation should imply an environment with stable exchange rates and increase incentives to invest in foreign markets. Inflation is measured as CPI CPI /CPI for month t. Assuming the series of inflation to be martingale, we estimate the expected inflation in month t as the realized inflation in month t 1.

10 3.1.2 Economic factors Bilateral trade Large value of trade between two countries should imply higher dependence between the countries and increase the degree of dependence. The variable of bilateral trade for country with country in year is calculated as,,,,, where, is the value of export from country to country in year, and, is the value of import to country from in year. In this way,, implies the value of trade between country and country relative to the total value of trade between country and all the countries except itself. Bilateral foreign direct investment Large value of bilateral FDI implies higher degree of exposures across the countries. The variable of bilateral FDI is calculated in the same manner as the variable of bilateral trade:,,,,, where, is the position of FDI outflow from country to country in year, and, is the position of FDI inflow to country from country in year. Similarity in industrial structure Countries with similar industrial structures are exposed to the same type of business risks. To construct a proxy for this factor, we can for example use the countries' exposures to

11 the ten world industry indexes. Same as Asgharian and Bengtsson (2006), we use the average absolute difference in exposures as a measure of the industry differences between every pair of countries Geographic factor Countries often have similar market structure and close economic relations with the nearby countries. It is plausible that the market volatility of a country affects its nearby countries to a larger extent. We use distances between capital cities to measure geographical distances between countries Defining neighborhood We use the medians of the bilateral variables (defined in section 3.1) of each market with other markets as benchmarks to define the neighbors of that market. For exchange rate volatility, absolute difference in expected inflation and similarity in industrial structure, small values should imply closeness between markets. Therefore, if the value is smaller than the median, these two countries are assumed to be neighbors. For bilateral trade, bilateral FDI and geographical distance, values of variables larger than median imply contiguity Selection of control variables In addition to assessing the spatial dependence of different markets using the attributes above, a number of explanatory macro variables are included in the model. These variables are changes in exchange rate, unexpected inflation, sovereign default rate and GDP growth. These variables are related to a country s business cycle and can affect the domestic equity market.

12 The change in exchange rate is calculated as the monthly difference of a country s exchange rate to USD. A positive change in exchange rate implies depreciation of this country s local currency, and is thus a proxy for economic distress. Therefore, we expect the change in exchange rate to have a negative impact on market returns and a positive impact on market volatility. Unexpected inflation is computed as realized inflation minus expected inflation described in Section 3.1. Positive unexpected inflation indicates economic boom, and can therefore be expected to have a positive impact on market returns and a negative impact on volatility. Sovereign default rate is measured on an ordinal scale between 1(AAA) and 20(CC) according to the Standard & Poor s foreign currency rating. A rise in sovereign default rate increases uncertainty and risk premium, so it should have a positive effect on market volatility and returns Data Sources We extract monthly and daily stock market indexes from MSCI from the end of 1994 to October 29, 2010 and construct the monthly returns and daily returns by taking log difference of the corresponding indexes. We construct the monthly returns by taking log difference of the monthly indexes. The market volatility is estimated as standard deviation of daily returns in each month.

13 We draw exchange rates from January 1995 to October 2010 from GTIS and WM/Reuters. The data are extracted from Datastream. We extract monthly CPI 3 from Datastream over the period January 1995 to October As for measure of industrial similarity, we collect the ten world industry indexes from Datastream. We get the exposure of a market to the world industry by regressing the returns of the market on the log-returns of each world industry index. Data of bilateral trade is drawn from STAN Bilateral Trade Database (source: OECD). The database presents the values of annual imports and exports of goods for all OECD counties and seventeen non-oecd countries, broken down by partner countries, thus providing data for all the countries in our study. The data covers the period 1995 to The values are presented in US dollars at current prices. We assume that the observations in 2010 the same with those in Data of foreign direct investment positions is collected from International Direct Investment Statistics (source: OECD). The Source provides annual bilateral FDI positions in U.S. dollars over the period 1995 to It reports the positions of outward FDI from OECD countries to OECD countries and non-oecd countries, as well as the positions of outward FDI from non-oecd countries to OECD countries. However, some observations are confidential. In addition, the observations on FDI from non-oecd countries to non-oecd countries are missing. We treat the values of the non-available observations as zeros. 3 CPI of Australia and New Zealand are not reported at monthly basis. We interpolate the reported quarterly CPI of Australia and New Zealand into the monthly series.

14 We collect data of foreign direct investment positions from OECD International Direct Investment Statistics. The Source provides annual bilateral FDI positions in U.S. dollars over the period 1995 to We relate the It reports the positions of outward FDI from OECD countries to OECD countries and non-oecd countries, as well as the positions of outward FDI from non-oecd countries to OECD countries. The observations on FDI from non-oecd countries to non-oecd countries are missing, however, the values of these observations are minor so we treat them as zeros. The data for foreign currency rating are collected from the Standard & Poor s Sovereign Rating and the yearly gross domestic product are from the World Bank. 4. Data Description There are 41 equity markets in our spatial analysis. Table 1 presents the selected markets and the descriptive statistics of their monthly returns over the period January 1995 to October A first observation is that Turkey has the largest returns on average. The maximum observation of Turkey is also the largest among all the markets. In comparison, Ireland has the smallest returns on average. Judge from standard deviation and range, Russian market has the highest level of risk, whereas the U.K. and the U.S. have relatively small risk. In addition, levels of skewness show that Korea has the fewest observations above its average while Belgium has the fewest observations below its average. Belgium also has the highest probability of extreme values. Japan is almost mesokurtotic. [Insert Table 1]

15 In order to obtain some prior knowledge of relationships among the selected markets, we present a world map depicting the monthly return correlations of the selected equity markets with the U.S market (see Figure 1). [Insert Figure 1] To give a simple illustration of our neighborhood matrices, we in Table 2 present the neighborhood of different markets with the US market according to the different factors. In this table the entire sample is divided in two sub-periods, from 1995 to 2002 and from 2003 to 2010, respectively. We use the average value of the variables over each subperiod to define the neighborhood. We use the medians of the bilateral variables of each market with the US as benchmarks, thereby 50% of the countries are assumed to be neighbor with the US. Canada, Hong Kong, Singapore and the UK, are related to the US based on most of the variables. On the other hand, some countries, such as Turkey, Russia and Czech republic, are quite weekly related to the US. According to the several variables, India has become closer to the US in the second period. Table 3 reports the proportion of overlapping ones between each pair of neighborhood matrices. Under the null-hypothesis that two different concepts of neighborhood are independent, the expected proportion is 0.5. A value of zero indicates that the respective definitions of neighborhood exhibit a perfectly negative correlation (neighborhood according to one definition implies non-neighborhood according to the other one). A value equal to one, on the other hand, indicates that the respective neighborhood definitions have a perfectly positive correlation (neighborhood according to one definition implies neighborhood according to the other one).

16 The table shows that almost all proportions are significantly different from 0.5, which indicates that there are systematic relationships between the various neighborhood definitions. However, the fractions are not particularly large, which shows that there are noticeable differences among the various neighborhood matrices. It is therefore worthwhile to separately analyze the dependencies among stock markets at proximate locations for each specific concept of neighborhood. 5. Empirical Analysis We analyze the spatial dependence among our selected markets over the entire sample period of January 1995 to October In order to rank the factors by their effects on spatial dependence, we not only investigate value and statistical significance of spatial autocorrelation coefficients, but also examine whether the spatial relationships defined by the selected factors outperform most of the possible spatial relationships. Furthermore, we compare the selected factors pair-wise by incorporating two factors simultaneously into the econometric model. In addition, in order to examine the changes in the spatial dependence over time, we divide the sample into two sub-samples, where the first subperiod is from January 1995 to November 2002 and the second sub-period is from December 2002 to October In addition, to investigate if the relationship among markets differs during a global distress periods comparing to the normal periods, we divide the sample based on the level of the monthly world volatility, using the volatility of the U.S. market as a proxy for the world-wide volatility. The high volatility period includes months when the volatility is higher than the median; whereas the low volatility period includes the remainder.

17 5.1. Estimated results over the entire sample period We present the empirical results for returns and volatility over the entire sample period in Table 4. The estimated :s of all the factors are highly significant and positive, implying positive spatial dependence among markets within the defined neighborhoods. Judging from the values of :s, we find that the ranking of factors for dependence among market returns is similar to the ranking for volatility. For example, markets that are close in terms of economic integration (except bilateral direct foreign investment) have larger dependence with one another in both returns and volatility than markets that are financially integrated or geographically close. Among all, the value of :s for industrial structure are the highest (0.92 for returns, and 1.10 for volatility), implying that markets similar in industrial structure tend to have the highest degree of spatial dependence. The second important factor is bilateral trade. As for the financial factors, exchange rate volatility plays a more important role in market dependence than expected inflation for both returns and volatility. The result is however mixed for geographical distance. It has a stronger effect than financial factors on volatility dependence, whereas it is worse than exchange rate volatility in explaining return dependence. We find bilateral foreign direct investment to be the worst factor in capturing spatial autocorrelation. This mainly results from the low quality of the data for foreign direct investment, which makes the contiguity matrix a bad measure of market relationships. In addition, because observations between several markets and many of their partner countries are missing, these markets have fewer than 20 neighbors, thus resulting in a smaller number of ones in the contiguity matrix compared with other factors. Therefore, the estimated tends to be smaller. [Insert Table 4]

18 In addition to :s, we also present the estimated :s that imply the degrees of spatial dependence among non-neighboring markets. For all the factors except foreign direct investment, the values of :s are much smaller than their corresponding :s. This is consistent with our expectation that neighboring markets have higher degree of dependence with one another than non-neighboring markets. However, we still find positive spatial dependence within most of the defined neighborhoods, as the values of :s are mostly positive. Only for industrial structure, is negative, implying negative spatial autocorrelation among markets with different industrial structures. The value for foreign direct investment is relatively large compared with the corresponding of. This may result from the low quality of the data for foreign direct investment, which makes the contiguity matrix a bad definition of relationships among markets and also leads to larger number of ones in than in. Furthermore, we find that the coefficients of most control variables are highly significant for both returns and volatility, except the coefficient of GDP growth for returns. This indicates that, in addition to spatial dependence, there is also significant spatial heterogeneity in returns and volatility among the selected markets. The signs of the coefficients are mostly consistent with the expectations discussed in section 3.3. For instance, a positive change of exchange rate has immediate positive impact on the market returns and negative impact on volatility. In addition, estimated is also presented. is the conditional mean of the U.S return or volatility, due to the inclusion of dummy variables for all the other markets. The estimated of returns is negative and insignificant for most of the factors, implying that the market returns can be mostly explained by spatial dependence and the control

19 variables. Only for industrial structure do we find to be statistically significant. As for volatility, the estimated is also negative for all the factors, however, it s statistically significant for most of the factors except expected inflation and geographical distance Evaluating the defined neighborhood As argued previously in this paper, the global trend international equity markets may result in positive spatial dependence even among markets that are not neighbors to one another. Therefore, in addition to examining the statistical significance of and, we also evaluate whether the spatial neighborhoods defined by the selected factors outperform other possible definitions of neighborhood. We randomly generate 200 contiguity matrices that have the same number of ones as our selected contiguity matrix and obtain 200 pairs of estimated and from the random matrices. Figures 2 and 3 depict the estimated values of :s and :s corresponding to our six selected neighborhood factors for returns and volatility, respectively. They also show the lower and upper 1%, 2.5% and 5% quantiles of the empirical distributions of and obtained from 200 randomly generated W-matrices. [Insert Figure 2 and Figure 3] As for returns, :s lie above the upper 1% quantile of the empirical distribution for all the factors except foreign direct investment. This suggests that these factors are better than 99% possible measures of market relationships in capturing the spatial dependence among our selected markets. In addition, the estimated :s are below the lower 1% quantile of the empirical distribution for these factors, implying that the markets that are

20 non-neighboring according to the selected factors have small degrees of spatial dependence compared with other possible definitions of neighborhood. As for volatility, only for the economic factors (excluding foreign direct investment) are economically significant above 1% upper quantile. The estimated for exchange rate volatility and geographical factor are between 2.5% upper quantile and 5% upper quantile. The estimated for expected inflation and foreign investment are not economically significant Comparison among factors In order to compare the bilateral factors explicitly with one another and rank them in terms of their importance to spatial dependence, we modify the econometric modeling by defining in a different way. We have the weighting matrix of one factor as and the weighting matrix of another factor as. In this way, we are able to compare factors pair-wise within the model. The factor with larger value of is better at explaining the dependence among markets relative to the other factor. We present the pair-wise comparison between factors by displaying the signs of differences between and in Table 5. A positive sign shows that the factor in that column has larger value of compared with the factor in the row. The comparison between factors presented in Table 5 is consistent with the previous findings in Section 4.1 and 4.2. For example, we find that industrial structure is superior to all the other factors in capturing dependence among both returns and volatility, as the difference between its between those of all other factors are positive. Bilateral trade is the second important factor, as it is inferior only to industrial structure. Geographical distance is

21 better than the financial factors and foreign direct investment in explaining volatility dependence, whereas it is less important than exchange rate volatility for dependence among market returns. [Insert Table 5] 5.4. Sub-period analysis In this section, we present the estimated :s for two sub-sample periods. As presented in Table 6, we find that the spatial dependence in returns tend to be higher during the first half of the sample period (until November 2002) than during the second half. With respect to the spatial dependence in volatilities, the picture is not as clear: Our results shown in Table 7 indicate that dependence in volatility among markets that are close in terms of economic integration or geographical distance are larger during the second half of the observation period, whereas dependence in volatility among markets that are close in terms of financial integration are larger during the first half of the sample period. Nevertheless, the ranking of the factors is still robust to the choice of sub-samples for both returns and volatility. [Insert Table 6 and Table 7] 6. Summary and Conclusions In this study we have analyzed dependence among financial markets with respect to both market returns and volatilities. We have applied spatial autoregressive models to investigate the linkages through which markets are connected with each other. Specifically, we have used monthly data on returns and volatilities for 41 markets

22 between January 1995 and October 2010 to assess six factors which potentially affect the dependence among markets. Except geographical neighborhood, which is typically assumed to affect spatial dependence, we have also considered three economic factors (bilateral trade, bilateral FDI, and similarity in industrial structure) and two financial factors (exchange rate volatility and differences in expected inflation) as potential sources of spatial dependence. Our main finding is that economic factors affect the dependence among financial markets to a greater extent than geographical neighborhood or financial integration. In particular, we find that a country s market return and volatility depend to a large degree on market returns and volatilities in countries that are similar in industrial structure and those that are important trading partners. We also find that, with respect to returns, the dependence among markets tend to be higher during the first half of the sample period (until November 2002) than during the second half. With respect to market volatilities, the picture is not as clear. References Anselin, L.,1988, Spatial Econometrics: Methods and Models, Dordrecht: Kluwer Academic Publishers. Anselin, L., 2006, Spatial econometrics, in: T.C. Mills and K. Patterson (Eds.), Palgrave Handbook of Econometrics: Volume 1, Econometric Theory. Basingstoke, Palgrave Macmillan, pp Anselin, L. and J. Le Gallo, Interpolation of air quality measures in hedonic house price models: Spatial aspects, Spatial Economic Analysis 1,

23 Asgharian, H., Bengtsson, C., Jump spillover in international equity markets, Journal of Financial Econometrics 4, Asgharian, H., Nossman, M., Risk Contagion among international stock markets, Journal of International Money and Finance 28, Baele, L., Volatility spillover effects in European equity markets, Journal of Financial and Quantitative Analysis 40, Bekaert, G., Harvey, C.R., Time-varying world market integration. Journal of Finance 50, Bekaert, G., Harvey, C.R., Emerging equity market volatility. Journal of Financial Economics 43, Bekaert, G., Harvey, C. R., Ng, A., Market integration and contagion. Journal of Business 78, Erb, C., Harvey, C.R., Viskanta, T., Forecasting international equity correlations. Financial Analysts Journal 50, Karolyi, G.A., Stulz, R.M., Why do markets move together? An investigation of U.S. Japan stock return comovements. Journal of Finance 51, Kelejian, H.H., Tavlas, G.S., Hondronyiannis, G., A spatial modeling approach to contagion among emerging economies. Open Economies Review 17, LeSage, J., Pace, R.K., 2009, Introduction to Spatial Econometrics, Boca Raton: Chapman & Hall/CRC. Longin, F., Solnik, B., Is correlation in international equity returns constant: Journal of International Money and Finance 14, 3 26.

24 Table 1. Descriptive statistics of monthly returns of the markets The table presents the markets included in the sample and the descriptive statistics of their monthly returns over the period January 1995 to October mean median Stdev. skewness kurtosis max min range Argentina Australia Austria Belgium Brazil Canada Chile China Czech Republic Denmark Finland France Germany Greece Hong Kong Hungary India Indonesia Ireland Israel Italy Japan Korea Malaysia Mexico Netherlands New Zealand Norway Philippines Poland Portugal Russia Singapore Spain Sweden Switzerland Taiwan Thailand Turkey U.K U.S Max Min

25 Table 2. Neighborhood with the US market based on different factors The table presents the neighborhood of different markets with the US market according to the different factors. In this table the entire sample is divided in two sub-periods, from 1995 to 2002 and from 2003 to 2010, respectively. We use the average value of the variables over each sub-period to define the neighborhood. The neighborhood is marked with x and non-neighborhood with -. The first/second mark is for the first/second period. Exch. rate vol. Inflation Ind. structure Trade Foreign invest. Geographical Argentina x x x Australia - - x - x x x - x x - - Austria x x x x Belgium - x x x x x x x - - x x Brazil x x x Canada x - x x x x x x x x x x Chile x - x x x x - - China x x - x - - x x Czech x x x Denmark - - x x x x x x Finland - x - - x x x France - x x x x x x x - - x x Germany - x x - x x x x x x x x Greece x x - x - x Hong Kong x x x x - - x - x x - - Hungary - - x x x x India x x - x x - x - - Indonesia - x x x - - Ireland x - x x x x x x Israel x x x x x x x - - Italy x x x x x x x x - - x x Japan x - - x x x x - - Korea x x x x x - - Malaysia x x - - x x x x x x - - Mexico - - x x x x x x x Netherlands - - x x x - x x - - x x New Zealand x x x Norway x - x - x x x Philippines x x x - x x - - Poland x x x x Portugal - x - x x x x x Russia x x Singapore x x x x x - x x x x - - Spain x x x x x x x x Sweden - - x - x x x x Switzerland - - x x x - x x x x x x Taiwan x x - x x x x x x x - - Thailand x x x x x x x - - Turkey U.K. x - x x x x x x x x x x

26 Table 3. The relationship between neighborhood variables The table shows the proportion of each neighborhood matrix which overlaps with all other neighborhood matrices. Under the null-hypothesis that two different concepts of neighborhood are independent, the expected proportion is 0.5. The significance test is based on a binomial distribution. Exch. rate vol. Inflation Ind. structure Trade Inflation 0.62 ** Ind. structure 0.65 ** 0.62 ** Trade 0.66 ** 0.56 ** 0.58 ** Foreign Investment 0.54 * 0.55 ** 0.56 ** 0.66 ** Foreign invest. Geographical Distance 0.60 ** ** 0.65 ** 0.64 ** * denotes statistical significance at 0.05 level. ** denotes statistical significance at 0.01 level and.

27 Table 4. Estimated results for returns and volatility over the entire sample period The table presents the estimated results from eq(1). means the degree of spatial dependence within each defined neighborhood, whereas implies the degree of spatial dependence among non-neighboring markets. ** denotes statistical significance at 0.01 level. The coefficients of the control variables and the conditional mean of the U.S. are also presented. Returns Exch. rate vol. Inflation Ind. structure Trade Foreign invest. Geographical 0.73 ** 0.61 ** 0.92 ** 0.83 ** 0.42 ** 0.63 ** 0.12 ** 0.23 ** ** 0.03 ** 0.40 ** 0.18 ** Exchange rate ** ** ** ** ** ** Unexp. inf ** ** ** ** ** ** Default rating ** ** ** ** ** ** GDP growth ** Volatility Exch. rate vol. Inflation Ind. structure Trade Foreign invest. Geographical 0.74 ** 0.66 ** 1.10 ** 1.03 ** 0.42 ** 0.75 ** 0.09 ** 0.16 ** 0.03 ** 0.09 ** 0.39 ** 0.06 ** Exchange rate ** ** ** ** ** ** Unexp. inf ** ** ** ** ** ** Default rating ** ** ** ** ** ** GDP growth ** ** ** ** ** ** ** ** ** ** ** denotes statistical significance at 0.01 level..

28 Table 5. Comparison of different neighborhood factors The table presents the results of the comparison between the estimated ρ and ρ for two alternative neighborhood matrices. Panel A, shows the results for returns and panel B for volatilities. A positive sign shows that the factor in that column has larger value of ρ compared with the factor in the row. A negative sign shows the opposite. Panel A. Exch. rate vol. Ind. Struct. Inflation Trade Foreign invest. Geographical Exch. rate vol. + + Ind. structure Inflation Trade + Foreign invest Geographical Panel B. Exch. rate vol. Ind. Struct. Inflation Trade Foreign invest. Geographical Exch. rate vol Ind. structure Inflation Trade + Foreign invest Geographical + +

29 Table 6. Estimated spatial autocorrelation coefficients for returns over sub-periods The table presents the estimated :s for returns using sub-sample periods based on calendar time and the level of the volatility of the U.S. market. Low volatility (high volatility) periods are the months with lower (higher) volatility than median. Exch. rate volatility Inflation Industrial structure Trade Foreign investment Geographical Entire period 0.73 ** 0.61 ** 0.92 ** 0.83 ** 0.42 ** 0.63 ** Jan Nov ** 0.67 ** 1.13 ** 0.84 ** 0.46 ** 0.66 ** Dec Oct ** 0.56 ** 0.85 ** 0.80 ** 0.40 ** 0.60 ** Entire period 0.12 ** 0.23 ** ** 0.03 ** 0.40 ** 0.18 ** Jan Nov ** 0.23 ** ** 0.07 ** 0.40 ** 0.20 ** Dec Oct ** 0.25 ** ** 0.18 ** Entire period 0.62 ** 0.38 ** 0.96 ** 0.79 ** ** Jan Nov ** 0.44 ** 1.18 ** 0.78 ** 0.06 ** 0.46 ** Dec Oct ** 0.32 ** 0.88 ** 0.78 ** ** ** denotes statistical significance at 0.01 level.

30 Table 7. Estimated spatial autocorrelation coefficients for volatility over sub-periods The table presents the estimated :s for volatilities using sub-sample periods based on calendar time and the level of the volatility of the U.S. market. Low volatility (high volatility) periods are the months with lower (higher) volatility than median. Exch. rate volatility Inflation Industrial structure Trade Foreign investment Geographical Entire period 0.74 ** 0.66 ** 1.10 ** 1.03 ** 0.65 ** 0.75 ** Jan Nov ** 1.02 ** 1.18 ** 0.79 ** 0.79 ** 0.71 ** Dec Oct ** 0.54 ** 1.52 ** 0.96 ** 0.53 ** 0.82 ** Entire period 0.09 ** 0.16 ** 0.03 ** 0.09 ** 0.48 ** 0.06 ** Jan Nov ** 0.21 ** 0.08 ** ** 0.43 ** 0.05 ** Dec Oct ** 0.36 ** ** ** 0.56 ** 0.27 ** Entire period 0.65 ** 0.49 ** 1.06 ** 0.94 ** 0.17 ** 0.69 ** Jan Nov ** 0.81 ** 1.11 ** 0.82 ** 0.36 ** 0.66 ** Dec Oct ** 0.18 ** 1.95 ** 1.04 ** ** ** denotes statistical significance at 0.01 level.

31 Figure 1. The world map depicting return correlation with the U.S. market The figure present a world map depicting the monthly return correlations of the equity markets in our sample with the U.S. market. We divide the correlations in four intervals: less than 0.5, between 0.5 and 0.6, between 0.6 and 0.7, between 0.7 and 1. There are approximately 10 countries in each interval.

32 Figure 2. The estimated and for returns compared to lower and upper quantiles of the empirical distribution of the estimated :s The figure depicts the estimated values of and for returns as dots. The lines denote the lower and upper 1%, 2.5% and 5% quantiles of the empirical distributions of and obtained from 200 randomly generated W-matrices Rho Rho2 1.0% 2.5% 5.0% Exch. rate vol. Ind. structure Inflation Trade Foreign investment Geographical

33 Figure 3. The estimated values of and for volatility compared to lower and upper quantiles of the empirical distribution of the estimated :s from randomly generated W matrices. The figure depicts the estimated values of and for volatility as dots. The lines denote the lower and upper 1%, 2.5% and 5% quantiles of the empirical distributions of and obtained from 200 randomly generated W-matrices Rho Rho2 1.0% 2.5% 5.0% Exch. rate vol. Ind. structure Inflation Trade Foreign investment Geographical