4.2  Quartile transitions

Transition matrices can be derived to provide some insight into how a firm’s sales per hour, purchases per hour and labour productivity typically evolve over time in relation to other firms. The transition tables that follow are derived as follows. In every year between 1994 and 2003 firms are grouped into quartiles according to their level of sales per hour, purchases per hour or labour productivity. In each case quartile 1 is comprised of the lowest quarter of firms in the distribution and quartile 4 the highest. Given a firm’s position in the distribution of a variable at a particular point in time, its position in that same distribution one, four and nine years later are then examined. It is not necessarily the case that firms are alive in both reference periods. To allow for this possibility, firms not in operation in any period are grouped into a category labelled ‘Out’. Examination of transitions between this category and the various quartiles of a variable’s distribution allow inferences to be drawn about the prevalence of firm entry and exit, and the persistence of relative sales per hour, purchases per hour and labour productivity respectively.

Table 10 describes the transition (relative) frequencies between quartiles of the sales per hour distribution. Panel A describes the average “1-year” transitions (i.e. between consecutive years); similarly, panels B and C describe the average “4-year” and “9-year” (i.e. between 1994 and 2003) transitions. The left most column in each panel indicates a firm’s position in the sales per hour distribution in a particular year, or whether it was not yet in operation (‘Out’). Similarly, the top row of each panel indicates the firm’s position in the distribution 1-, 4- or 9-years later (or if it was no longer in operation). Each row of the table must sum to one because at any particular point in time a firm must either be in a quartile of the sales per hour distribution or not in operation. The table entries are averages across the relevant years between 1994 and 2003 and indicate the proportion of firms in various sales quartiles, or that are no longer in operation, given that they previously belonged to a particular sales quartile or were not yet in operation.

If there is a strong positive association between firms’ sales per hour in consecutive periods there should be a relatively high proportion of firms in the diagonal elements of the table. Conversely, if there is a negative association between firms’ sales per hour in consecutive periods there should be a relatively high proportion of firms in the off-diagonal elements. If no association exists between sales per hour in consecutive periods, the frequencies should be similar across the cells.

If there is a positive association between the prevalence of firm entry or exit and sales, the proportion of firms in the cells of the bottom row and right most column of the table should increase from left to right and top to bottom respectively, ignoring the cell at the bottom right of the table.[14] Conversely, if there is a negative association between the prevalence of firm entry or exit and sales, the proportion of firms in cells should decrease from left to right and top to bottom respectively. If no association exists, frequencies should be similar across the bottom row and similar across the right most column of the table.

Panel A of table 10 shows that, in general, relatively high proportions of firms in sales per hour quartiles in a particular period belong to the same quartile of the sales per hour distribution a year later. The proportion of firms in the sales per hour quartiles a year later tends to decline the more distant it is from the sales per hour quartile a year earlier. For example, of firms initially in the bottom sales per hour quartile, around 77 percent are also in the bottom sales per hour quartile a year later while only 1 percent are in the top quartile.

Panel B of Table 10 shows lower proportions of firms on the diagonal for the 4-year transitions compared to the 1-year transitions. On average, the proportion of firms who are in the same quartile for sales per hour as they were four years earlier is around 54 percent. This compares to around 73 percent of firms being in the same quartile for sales per hour as they were one year earlier. The negative association between the prevalence of both entry and exit and sales per hour also seems to be weaker, although not surprisingly far higher proportions of firms enter and exit over four years than over one year.

The 9-year transitions in panel C of Table 10 show that about 40 percent of firms in existence in 1994 are in the same sales per hour quartile in 2003. This is lower again than the equivalent average for the 4-year transitions. It is also now difficult to see any relationship between the prevalence of firm entry and exit, and sales per hour. The patterns in Table 10 suggest there is a positive association between sales per hour in consecutive periods. There also seems to be a negative association between the prevalence of both entry and exit, and sales per hour. In other words firms appear more likely to enter and exit with low levels of sales per hour.

Table 11 similarly shows the 1-, 4- and 9-year transition probabilities for purchases per hour. Apart from a weaker relationship between firm entry and purchases per hour than that for sales per hour, the patterns here look very similar. On average the proportions of firms that are in the same quartile for purchases per hour as they were one, four and nine years earlier are around 73, 53 and 38 percent respectively. As for sales per hour, the amount of movement by firms across the distribution of purchases rises over time.

Table 12 shows 1-, 4- and 9-year transitions for labour productivity. The patterns here look somewhat different to those for sales per hour and purchases per hour. In general, lower proportions of firms belong to the diagonal elements of these tables than those for sales or purchases per hour. On average the proportions of firms that are in the same quartile for labour productivity as they were one, four and nine years earlier are around 62, 44 and 33 percent respectively. The negative association between the prevalence of firm entry and exit, and labour productivity looks to be slightly stronger however. In other words, firms look more likely to enter or exit with low levels of labour productivity, a characteristic also noted by Law and McLellan (2005).

In summary, the relative rates of firms’ sales per hour and purchases per hour display quite high year-to-year persistence. Around 73 percent of firms remain in the same quartile of sales per hour and purchases per hour from one year to the next. Even after nine years around 40 percent of firms are in the same quartile. Relative rates of labour productivity are somewhat less persistent for one year transitions, although around 62 percent of firms remain in the same quartile after one year. After four years this percentage drops to around 43 and after 9 years it drops to around 33.

Although these transitions rates suggest a high degree of persistence, the limited amount of international evidence that does exist suggests that persistence is to be expected. For instance, Bartelsman and Dhrymes (1998) find that for US manufacturing plants, more than one-third of plants remain in the same quintile after five years. Baily, Hulten and Campbell (1992) used a sample of 23 four-digit SIC industries and, when weighted by employment in each plant, found that about 20 percent of employment remains in its original position after ten years. Compared to rates of transition for US manufacturing, New Zealand firm transition rates may be a little lower, but what is clear is that a high degree of persistence is not unusual.