3.3  Association between labour productivity and its components

The dispersion in labour productivity across firms may be related to the size of the firm, as proxied by their total hours, sales or purchases. To evaluate this possibility, we grouped firms into quartiles according to their level of labour productivity in any given year, where quartile 1 is comprised of the lowest productivity firms and quartile 4 the highest. Given a firm’s position in the labour productivity distribution at a particular point in time, its position in the distribution of other variables at the same point in time is then examined. Table 7 provides these relationships.

Table 7A shows how the distribution of labour productivity relates to that of total hours worked or the labour input of firms. The left most column of the table indicates a firm’s position in the labour productivity distribution while the uppermost row of the table indicates a firm’s position in the distribution of total hours worked. Quartile 1 in both cases refers to the lowest quartile of the distribution and quartile 4 the highest. Each row and column of the table must sum to one as once in a labour productivity or labour input quartile a firm must lie somewhere on the labour input or labour productivity distribution respectively. Figures in Table 7 are averages for the ten years between 1994 and 2003 and indicate the proportion of firms in various labour input quartiles given they belong to a particular labour productivity quartile.

If there is a positive association between a firm’s labour productivity and labour input there should be a relatively high proportion of firms in the diagonal elements of the table. Conversely, if there is a negative association between a firm’s labour productivity and labour input there should be a relatively high proportion of firms in the off-diagonal elements. If no association exists between labour productivity and labour input, the proportions should be similar across the table.

In general, relatively high proportions of firms in labour productivity quartiles belong to the same quartile of the labour input distribution. The proportion of firms in labour input quartiles tends to decline the more dissimilar that labour input quartile is to the labour productivity quartile. For example, of those firms in the bottom labour productivity quartile around 36 percent are also in the bottom labour input quartile while only 16 percent are in the top quartile. The pattern exhibited in panel A of Table 7 suggests there is a weak positive association between labour productivity and labour input.

Table 7   Association between labour productivity and measures of firm size (contemporaneous: average of 10 years)

The relationship between the distributions of labour productivity and sales and between labour productivity and purchases are shown in panels B and C of Table 7 respectively. In general, higher proportions of firms belong to the diagonal elements of these tables than is the case for the labour productivity and total hours worked relationship. On average, the proportion of firms who are in the same quartile for labour productivity as they are for sales is around 39 percent. This compares to around 32 percent of firms being in the same quartile for labour productivity as they are for labour input. On average the proportion of firms who are in the same quartile for labour productivity as they are for purchases is around 37 percent.

There appears to be a positive association between labour productivity and each of sales, purchases and labour input, all of which can be thought of as a crude measure of the scale of a firm’s production. This is perhaps suggestive of increasing returns to scale. However, to be certain that this reflects scale effects, one would need to control for the effects of other factors likely to impact on firm labour productivity such as capital, inputs.

The relationship between the distributions of labour productivity and its numerator, value-added, is shown in Table 8. On average the proportion of firms who are in the same quartile for labour productivity as they are for value-added is around 47 percent. This relatively high average is mostly due to 70 percent of firms in the bottom quartile and 48 percent of firms in the top quartile of the labour productivity distribution also being in the bottom and top quartiles of the distribution of value-added respectively.

Table 9 shows how the distribution of labour productivity relates to that of the sales per hour and purchases per hour of firms respectively. In Table 9A, on average the proportion of firms who are in the same quartile for labour productivity as they are for sales per hour is around 48 percent. Recall from Section 2.1 that there are alternative ways to construct labour productivity from this database, one of which is simply to divide total sales by total hours worked. On average more than half the firms are in different sales per hour quartiles relative to their labour productivity quartile. This suggests that the choice of labour productivity measurement may impact on conclusions.

The relationship between the distributions of labour productivity and purchases per hour is shown in 9B. On average the proportion of firms who are in the same quartile for labour productivity as they are for purchases per hour is around 37 percent.

Table 9   Association between labour productivity and sales per hour worked and purchases per hour (contemporaneous: average of 10 years)