*4.4. Correlation Analysis*

In this section, we examine the cross-sectional correlations between the spread benchmarks and the spread proxies. The correlation is calculated across firms in each country group for each pair of spread benchmark and spread proxy. The correlations with both a predicted sign and statistical significance at the 5% level are indicated with \*\*. In addition, if the correlation is greater than 0.50, it is

further indicated with a bold color. We consider that, even if somewhat arbitrary, a correlation of 0.50 or greater is a good indication that the proxy captures the benchmark reasonably well.

Panel A of Table 4 reports the pairwise correlation between the spread proxies (*ROLL*, *HASB*, and *LOT*), and the spread benchmarks (*ES*, *QS*, and *RS*) for each stock group from G1 to G4. It is clear that *LOT* dominates both *ROLL* and *HASB*. The correlation between *ROLL* and the spread benchmarks are in general between 0.20 and 0.40. The same conclusion can be drawn for *HASB*, except in Group G2.<sup>8</sup> The correlation between *LOT* and the spread benchmarks are much higher. In general, the correlations are between 0.50 and 0.80 for all four stock groups from G1 to G4. In the unreported results, we repeat the correlation analysis on a country-by-country basis. Overall, the results confirm that the *LOT* measure tends to do better than either *ROLL* or *HASB*. The evidence from the correlation structure is consistent with that based on measurement error at the individual stock level from Panel A of Table 3.

**Table 4.** Cross-Sectional Correlations between Liquidity Benchmarks and Liquidity Proxies. All countries are partitioned into four groups (G1 to G4) based on the average daily turnover of each country. Panel A of the table reports the Spearman cross-sectional correlations between spread benchmarks (*ES*, *QS*, and *RS*), and spread proxies (*ROLL*, *HASB*, and *LOT*). Panel B reports the Spearman cross-sectional correlations between price impact benchmarks (*LAMBDA*, *IMP*, and *ASC*), and price impact proxies (*AMIHUD*, 1/*AMIVEST*, and *PASTOR*). Among the spread proxies that have a significant correlation, the ones larger than 0.50 are in bold. The sample covers 1183 firms from 21 emerging markets. The sample period is from February to May 2004. \*\* indicates statistical significance at the 5% level.




<sup>8</sup> The generally low Spearman correlations of the HASB estimate are somewhat unexpected. Hasbrouck (2009) reports a Spearman correlation of 0.89 for the U.S. markets. The difference might be due to differences in liquidity characteristics between the U.S. and emerging markets.

Panel B of Table 4 presents the pairwise correlations between price impact proxies (*AMIHUD*, 1/*AMIVEST*, and *PASTOR*), and price impact benchmarks (*LAMBDA*, *IMP*, and *ASC*). Two clear patterns emerge. First, there is no clear winner among the three price impact proxies when we examine their correlations with price impact benchmarks. Therefore, evidence from the correlation structure confirms the evidence from the measurement error in Panel B of Table 3, regarding the effectiveness of price impact proxies. Second, in the more liquid markets of Groups G1 and G2, the correlation between the price impact proxies and *LAMBDA* is much higher than the correlation between price impact proxies and either *IMP* or *ASC*. Third, the performance of *PASTOR* is as good as either *AMIHUD* or 1/*AMIVEST*. This result is in contrast to the findings by Hasbrouck (2009) and Goyenko et al. (2009), although these two studies draw their conclusions from the U.S. market.
