the correlation measures within industry-pair across-countries, and within-country across industrypairs. The former is a measure of the typical variation of correlations across industry-pairs and the latter a measure of the typical variation of correlations within a country.<sup>10</sup> The table shows that both measures exhibit considerable variations in the within and between dimensions, although the latter is somewhat smaller than the former. The bottom two rows also show that the typical withinindustry and within-country variations in correlations are similar, and, only slightly reduced by partialling-out industry-pair and country fixed effects. This indicates that an important component of the variation of the correlations is idiosyncratic (within industry-pair and country). On one hand, this is good news for the identification of the mechanism because it focuses precisely on the within-country across industry-pairs variation of the data, but on the other hand it could just mean that correlations are noisily estimated and that the standard deviation of the correlations in the sample is a demanding metric to gauge the economic relevance of the estimates.

# 4.3 Input-Output linkages

A central assumption of this paper is that input-output linkages between industries are largely technologically determined, based on which the linkage measures obtained in a country with good available information, like the U.S., can be extrapolated to the rest of the countries in the sample. The main reason for assuming a constant distance across industry pairs is the lack of comparable information on input-output relations for a broad set of countries at a good level of aggregation; OECD data on input-output matrices cover only 20 countries and 20 manufacturing sectors and data from Olarreaga and Nicita (2004) _Trade and protection database_ covers a larger number of countries but divides manufactures in 17 sectors only and lacks some key variables required to construct the distance matrices. Nevertheless, this assumption should be relatively uncontroversial because, by construction input-output matrices reflect technological links across sectors, and, therefore, their variation across countries is likely to be limited. Table 5 and Figure 1 provide some evidence in this regard. Table 5 reports the variance decomposition of the Direct Requirement Matrices, a crucial input on the construction of the distance measures, obtained from Olarreaga and Nicita (2004) for 67 countries. Although the level of aggregation is different from the one used in this paper, the table makes apparent that almost all the variation in the direct requirement matrices is within country, across industry-pairs. Additional evidence in support of this assumption comes from Figure 1, which plots the _input-output distance_ built using U.S. data as described below and the same distances estimated using U.K. data. The relation between the two measures is striking (the correlation is 0.98).

Under the assumption of technologically determined links, I build the matrix _D_ of contempo-

> 10For any variable _xic_ with variation across industry pairs ( _i_ ) and countries ( _c_ ), the within country variation corresponds to the standard deviation of _xic − x_  ̄ _.c_ +  ̄ _x.._ , where the dot represents the average in that particular dimension.  ̄ The between-countries variation therefore corresponds to the standard deviation of _x.c_ . The within industry-pairs, across-countries variation is computed as follows: for each industry-pair, I first calculate the standard deviation of its correlation across the countries in the sample and then compute the average of these standard deviations across all industry-pairs. I compute the within-country, across industry-pairs variation similarly by switching the order of aggregation.

15