Tables 3.1, 3.2, 3.3 and 3.4 attempt to illustrate how the representativity of the sampling frame changes with respect to the complete case and the sample with replacement.<sup>17</sup> In all cases, the percentages vary slightly in the complete case with respect to the sampling frame. The percentages of the sample with replacement are more similar to the sampling frame. For instance, in India from Table 3.1, panel a), the percentage of ‘ _food_ ’ firms falls from 8.7% to 6.9%, while after the replacement it is 7.9%. Symmetrically, the percentage of ‘ _apparel_ ’ firms jumps from 12% to 14.3% in the complete case and to 12.4% in the sample with replacement. Similar patterns can be observed in the remaining countries. Finally, from these tables response rates do differ across countries, but within countries they are remarkably uniform across regions and industries.

Table 3.1: INDIA, Representativity of sampling frame, complete case and sample with replacement

||Sampli|ng frame<sup>(a)</sup>|Comp|lete case<sup>(b)</sup>|With r|eplacement<sup>(c)</sup>|
|---|---|---|---|---|---|---|
||# Obs|Perc over total|# Obs|Perc over total|# Obs|Perc over total|
|||**a) by Ind**|**ustry**||||
|Food|597|8.7|307|6.9|454|7.9|
|Textiles &Leather|888|13|600|13.5|738|12.8|
|Apparel|825|12|634|14.3|715|12.4|
|Chemicals & Chemicalprds|930|13.6|610|13.7|769|13.4|
|Plastics &Rubbers|480|7|316|7.1|411|7.1|
|Non-metallic products|216|3.2|110|2.5|164|2.9|
|Structural metal&metalprds|909|13.3|480|10.8|771|13.4|
|Machinery &Equipment|2,004|29.3|1,391|31.3|1,728|30.1|
|Total|6,849|100|4,448|100|5,750|100|
|||**b) by s**|**ize**||||
|Small|3,621|52.9|2,247|50.5|2,953|51.4|
|Medium|2,271|33.2|1,537|34.6|1,968|34.2|
|Large|957|14|664|14.9|829|14.4|
|Total|6,849|100|4,448|100|5,750|100|

Notes: (a) “Sampling frame” refers to the total number of observations (firms surveyed multiplied by the number of years of information).

(b) “Complete case” refers to the complete case of production function variables (sales, materials, capital and labor), missing values in other IC variables—other than production function— are not considered.

(c) “With replacement” refers to the sample after imputing IC variables according to the ICA Method; missing values in other IC variables—other than production function—are not considered. Notice that only observations with information available in at least one of sales, labor, labor cost, materials or capital, are imputed Source: Authors calculations with ICSs data.

> 17 In order to evaluate how representativity changes from the sampling frame to the complete case, we would need to have information on the weight of each category over the reference population. Unfortunately, this information is not available. As second best, we can still demonstrate how representativity changes from the data we have. Let us suppose population is split into two strata, and that the original sample selects a given number of observations for strata 1 and 2, and as a result X and Y are the percentages that represent the weight of each strata in the population. In the complete case, we introduce the missing data problem so instead of X and Y we have X ́, Y ́. If we suppose that the sampling frame is representative of the population then the complete case is said to be representative if, and only if, the weights in the complete case are proportional to the weights in the sampling frame; that is X≈X ́ and Y≈Y ́.

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