Summary Statistics. The test statistic for hypothesis testing is a quantity derived from the sample in or- der to measure the compatibility between the null hypothesis and the sample data, and determine whether this null hypothesis should be rejected or not. Test statistics developed from a likelihood ratio are optimally powerful according to the Xxxxxx- Xxxxxxx lemma, under certain conditions. Other types of test statistics, however, may also be useful even if not theoretically optimal. A statistic that is interpretable and captures the differences between the observed data and the null-hypothesized models may indeed be useful. Conventionally, hypothesis testing utilizes test statistics whose exact or approximate theoretical null distribution is known under certain strong assumptions of the data such as normality. The permutation test, nevertheless, has an important property of allowing the use of non-standard test statistics with unknown or complicated null distribution (Xxxxxxx et al., 2014). Owing to this key feature of permutation test, we also considered employing the useful whole-image summary statistics as test statistics in addition to cluster statistics for the analysis of the imaging data: the unweighted (h2) and variance-weighted (wh2) averages of all voxel-wise heritability estimates, the second (Q2, the median) and third (Q3) quartiles of these estimates, mean of those heritability estimates greater than Q2 (h2(Q2)), and mean of those heritability estimates greater than Q3 (h2(Q3)). These statistics emphasize the right “tail” (e.g., we omit the first quartile Q1), as exact-zero h2 values make interpreting the left “tail” difficult. If we assume that there are totally K in-mask voxels within the ROI’s, these mean statistics are defined as follows: h2 = 1 Σ h2, K r=1 wh2 = 1 Σ . σ2, σ2Σ h2, σ2 = 1 Σ σ2, K r=1 2(Q ) = #{h2 > Q2} K r=1 2(Q ) = #{h2 > Q3} where σ2 and h2 denote the voxel-wise phenotypic variance and the corresponding heritability for voxel r (r = 1, . . . , K). The permutation inference can be implemented rapidly using these summary stat- istics, their empirical null distribution can be formed by permutation test, and the corresponding permutation-based p-values can be obtained using these null distri- butions. The fast implementation of these summary statistics provides a tool for exploring the whole brain quickly and a significant result with p-values less than the given level α implies that there should be some significantly heritable brain regi...
Summary Statistics. Table 2, Panel A reports the summary statistics of fund manager and fund attributes for the full sample. The mutual fund managers’ age distribution is similar to that of earlier papers, with a standard deviation of 9.38, but the average age of 46.2 is higher by 2 to 3 years. On average, the manager level termination probability is 13%, which is lower than what previous literature finds based on fund level termination. Fund managers whose age is above 60 amount to 9% of the fund manager population. Female fund managers also consist of 9% of the total population, and about 60% (56%) of the fund managers have CFA (MBA) degree. Net inflows to funds are on average 7%, with a median value of negative 5%. My main variable of interest, Tracking Error, has a mean of 1.19% (1.41%) with 0.7% 10The data on Active Share is available from the website of Xxxxx Xxxxxxxxx at xxxx://xxx.xxxxxxxxx.xxx/data.html (0.99%) standard deviation at a monthly frequency when estimated using Xxxx-Xxxxxx- Xxxxxxx 4 Factor model (One Factor model with combination of Objective index and S&P 500 as factor returns). The distribution of log fund TNA is highly skewed, as evidenced in the literature, with a mean of 19.55 and standard deviation of 1.64. The log of fund family TNA is also highly skewed, with a mean of 23.32 and a standard deviation of 2.23. Panel B (C) reports the same statistics for a subset of junior (senior) fund managers and their funds. Junior (senior) fund managers are defined as managers with age in the bottom (top) 40th percentile of each cross section. The age gap between average fund manager in the junior group and in the senior group is 18 years. Other notable differences are that funds managed by junior managers receive higher net inflows than the funds managed by seasoned managers. Also, on average, junior fund managers tend to have higher Tracking Error. Panel D (E) reports summary statistics for funds during the the earlier period (more recent period). Most of the fund manager and fund attributes have changed significantly between these two periods. The most notable difference is the increase in termination probability. While the termination probability at an annual basis was 7% during the earlier period, it has become 14%in the more recent period. Also, average net inflows have de- creased from 14% in the earlier period to 5%in the more recent period. Lastly, the measure of risk taking has decreased for both measures of Tracking Error.
Summary Statistics. Table 2.1 depicts the summary statistics. On average the value of a country's sectoral exports amounts to 5,761,478 US$ per year and is led by China, which has an average export value above 1 billion US$ in the "Electrical and Machinery" sector for the year 2013 until 2015. Our variable of interest, a sectoral productivity shock in a country due to disruptions transmitted over the supply chain, lies between 0 and 1 with an average value of 0.399 for a country, sector and year. The proxy for foreign competition, measured as output weighted disasters abroad per sector, country and year, varies between 0.061 and 0.824, where the maximum of a foreign competition shock is in the "Electricity, Gas and Water" sector in the year 1997. Finally, a sector's size and export experience might affect its ability to cope with a productivity shock transmitted over the supply chain. The gross output of a given sector, which serves as a measure of sectoral size, is led by China's "Electrical and Machinery" sector. Our measure of export experience, a country's sector exports relative to the world exports in the previous year, is on average 1% and lead by France's "Electricity, Gas and Water" sector, which had an export share of around 54% in the year 1996. In Table 2.2 the number of observations per world region and sectoral group are shown. The manufacturing sector is in all world regions the sector where most countries are active each year, which is then followed by the agricultural sector. The energy sector is the least traded sector. All in all, Table 2.2 makes us confident that we have enough observations per country, 32 xxxxx://xxx.xxxxx.xx/ sector and year to identify the impact of supply chain shocks on a country sector's export performance.
Summary Statistics. Figure 1 plots the increase in dollar value of net repurchase from 1988 through 2006, while Figure 2 shows the normalized value by the aggregate market capitalization of all firms and that of repurchasing firms in the same time period. Aggregate repurchases peaked in 1999 beginning from the end of 1980s, and then dropped slightly afterwards. However, since 2003 there has been an increase, with the most dramatic increase occurring through 2006. By the end of 2006, the total dollar value of net repurchases had almost tripled from its historical peak in 1999. Similar to Xxxxxxx and Xxxxxxx (2008), we find that the market-cap normalized net repurchase value moves in pace with the stock market and business cycles and also indicates the intensiveness of repurchase activity in the middle and through the end of 1990s and after 2003. Overall, consistent with the literature (x.x. Xxxxxxx and Xxxxxxxx (2002) and Xxxxxxx (2008)), Figures 1 and 2 demonstrate that share repurchases have become an increasingly significant payout mode, even after the dividend tax cut in 2003. In addition, the sharp increase in repurchases since 2003 suggests that the initiation and increase in dividend payments following the Jobs and Growth Tax Relief Reconciliation Act may not have come at the expense of a reduction in share repurchases. Figure 3 plots the proportion of firms that make open-market repurchases by year. We examine separately firms that make repurchases only and firms that engage in both repurchasing shares and paying dividends in a given year. Before 1997, the proportion of firms that made repurchases only does not differ from that of firms that paid out cash through both repurchases and dividends. Yet during 1997-2006, there is a high growth in the fraction of firms that repurchased shares without paying dividends, even though the growth rates vary over time and seem to be correlated with stock market valuations. The evidence in Figure 3 strengthens the finding in Figures 1 and 2 that share repurchases have been an increasingly significant phenomenon. Table 1 provides summary statistics for the 55035 firm-year observations for 6291 firms from 1987 through 2006. As shown in Panel A, an average firm makes net repurchases once every five years. The annual net repurchases are valued at about 3.4% (median 1.9%) of the firm’s market value of equity, 7.3% (median 3.8%) of the firm’s book value of equity, and 3.6% (median 1.8%) of the firm’s book value of total assets. Panel B of...
Summary Statistics. Table 1 reports the summary statistics for our main variables. Panels A and B include the country-level variables for country pairs and firm-level variables for foreign partners, respectively. In Panel A, we observe that the average ratio of the number of SOE-involved cross-border alliances between two countries (average 0.304%) is lower than the ratio of the number of alliances with non-SOE partners (average 1.190%). This result is consistent with Xxxxxxx and Xxxx (2017)’s finding in the context of acquisitions as they report that the corporate acquirer deal ratio is higher than the government-controlled acquirer deal ratio. As for the country-level factors which measure the differences between the country-pairs, e.g., “Polity IV democracy diff”, the mean value of such factors shown is zero, which is due to the fact that the country-pair-year observations in our sample include both, for instance, Country A - Country B pair and Country B - Country A pair.23 Panel B shows the characteristics of the firms, which 23 That is, we have both Country A - Country B pair and Country B - Country A pair which represents the deals between these two countries but happened in Country A and Country B, respectively. The variable for the Country A - Country B pair observations is measured as the value in Country A minus Country B, whereas for the Country B - Country A pair observations is the value in Country B minus Country A. are defined as foreign partners in cross-border alliances.24 We observe that around 20% foreign firms are in the same industry as the local partners, and on average, the foreign partners in our sample have around $ 4.521 billion total assets in the year before they form an alliance. Besides, Panel C of Table 1 presents the distribution of cross-border alliance activities across countries. The top 20 countries are reported in descending order by the total number of local SOEs involved in cross-border alliances in a particular country from 1990 to 2018. China has the largest total number of cross-border alliances with local SOEs (718 deals, accounting for 27.23% worldwide), followed by Hungary, Russia, and India. We also notice that some emerging countries are more likely to have SOEs than non-SOEs collaborating with foreign firms. For instance, more than 70% deals in Algeria and Czech involve local SOEs in cross- border alliances, followed by Cuba (63.04%), Hungary (59.43%) and Venezuela (46.05%). In these countries, foreign partners are more likely t...
