2.3 Weighting
The means, medians and standard deviations of key variables used in our analysis are presented in Table 3. The table compares estimates that are unweighted (i.e. each firm-year observation contributing equally), weighted by the firm’s annual total hours, and weighted by the firm’s mean annual total hours over its lifetime. Weighting better reflects the productive capacity of different firms, by giving greater importance to large versus small firms. Weighting generally increases the means and medians for employment hours, sales per hour, purchases per hour, and value-added per hour. The choice between a time varying and a time invariant weight also makes a difference to the summary statistics. All our subsequent analysis is weighted, using the mean annual total hours worked for each firm over its lifetime within the sample period.
| Unweighted | Weighted (hours) | Weighted (mean hours) | |||||||
|---|---|---|---|---|---|---|---|---|---|
| Variable | Mean | Median | SD | Mean | Median | SD | Mean | Median | SD |
| Hoursa | 11.28 | 3.08 | 124.63 | 1389.13 | 54.82 | 3483.80 | 1317.47 | 47.73 | 3392.06 |
| Sales / hourb | 100.82 | 38.76 | 1875.80 | 112.45 | 55.71 | 720.57 | 151.26 | 57.98 | 1539.06 |
| Purchases / hourb | 68.39 | 20.33 | 1685.36 | 80.11 | 30.75 | 656.63 | 112.21 | 32.40 | 1449.26 |
| Labour productivityb | 32.47 | 14.31 | 492.49 | 32.40 | 19.91 | 201.94 | 39.13 | 20.74 | 284.74 |
Notes to Table 3: a = thousands, b = single units.
2.4 Other Issues
There are a number of potential problems with the various data sources used and the data set constructed from them that may, among other things, reduce the reliability of the estimated proxy for labour productivity. One is the fact that sales and purchases of capital goods are included in the variables that measure firms’ sales and purchases. The typically infrequent and lumpy nature of capital transactions means that measures of value-added for individual firms could be quite volatile from period to period and could even be large negative values, with corresponding negative measures of labour productivity. In fact about 13 percent of firm-year observations on labour productivity are negative.
Another potential problem could arise with the assumed timing of transactions used to calculate value-added. For all firms in every year, value-added is calculated as sales in that year less purchases in the same year. For many firms, however, sales may in fact lag purchases. Further, the timing of sales versus purchases may differ across industries or even across firms within industries.
There are other data limitations. First, small enterprises that have GST sales below $30,000 are excluded from the BD. Second, company restructures and changes of ownership that are accompanied by new GST registrations will result in enterprise births and deaths even though these pertain to existing enterprises. Therefore, enterprise births and deaths may reflect administration changes in addition to genuine business start ups and closures.[12] Third, employment data are for a point in time, while sales and purchases data are on an annual basis. Fourth, for entering and exiting firms in particular, sales and purchases data were not always available for the entire year of entry or exit and had to be annualised.
These limitations mean that any results using this data should be interpreted with a degree of caution. They also highlight the need for careful examination of the properties of these data.
Notes
- [12]Although the BD does not control for ‘false’ births and deaths owing to enterprise administrative changes, the development of the Linked Employer Employee Database (LEED) is attempting to do this.
