3.2 Product Sales Distribution within Firms

Theoretical models have different predictions about the distribution of product sales across products within firms. According to Nocke and Yeaple, output is evenly distributed across products since firms do not have different product-specific expertise. Bernard et al. (2006b), on the other hand, assume that output will be highly skewed towards products for which firms have particular expertise.

Table 5 shows the distribution of products within New Zealand exporters by reporting the average share of a product in the total value of exports of a multi-product firm. The results show that output is not evenly distributed across products. Each row refers to the within-firm ranking of a product by the product's contribution to total exports of the firm. Each column denotes the firms producing the number of products shown at the top. Only firms producing 10 or fewer products are considered. Exports are highly skewed towards the main product. The share of the largest product declines as the number of products exported by a firm increases. The share of the main product declines from 75% for 2 product exporters to 59% and 52% for 5 and 10 product exporters , respectively. For the US, the numbers are 80%, 58% and 46% for 2, 5 and 10 product firms, respectively. These results give support to the predictions of the model by Bernard et al. (2006) which assumes that output will be skewed towards those products for which firms have a comparative advantage in.

Note: Columns indicate the number of products produced by the firm. Rows indicate the share of the product, in decreasing order of size. Each cell is the average across the relevant firm-products in the sample (1996-2005).

Firm size distribution literature uses a Pareto distribution, which predicts a log linear regression of log rank of firm shipments on log firm shipments, as a benchmark. Similarly, to assess the product-size distribution within firms producing the same number of products, we estimate an OLS regression of log rank of firm-product size on the log of their share of exports (derived in Table 5). The fitted and actual values for product rank and size are shown in Figure 1. We observe that the actual values lie above the fitted values in the middle of the distribution and below the fitted values in the tails, implying thinner tails than the Pareto distribution. This suggests that heterogeneity across products within firms is analogous to heterogeneity across firms in the firm-size distribution literature.

Figure 1 - Within-Firm Product Size and Rank

Note: The solid line plots within-firm product rank against within-firm product size (from Table 5). Each panel is for the set of firms with the noted number of products. Fitted lines are the result of an OLS regression of log product rank on log product size.

Figure 2 extends the analysis to all firms, that is, firms exporting more than 10 products, to show that the value of exports across products is not symmetric. As the number of products increase, the share of the largest product decreases, but the relationship is not perfect. This suggests that for firms with multiple products, they will have at least one major product that they export, and a number of smaller products that they export on the side.

Figure 2 – Average Share of the Largest Product

Note: The export value share of the largest product is plotted against the number of products.