6 Concluding discussion
Internationally, longitudinal firm unit record databases provide a rich source of information for analysing firm productivity. Statistics New Zealand’s Business Demography (BD) and Goods and Services Tax (GST) databases have similar potential yet little is known about their properties. The aim of this study has been to gain a better understanding of the characteristics of the BD and GST data with particular attention being given to measures of labour productivity and its components.
Results reveal a great deal of heterogeneity in each of sales per hour, purchases per hour and labour productivity across industries. Differences across cohorts are less pronounced. Consistent with the findings in the international literature, within each industry or cohort, differences across firms are large. For example, in the case of one industry the firm at the 75th percentile of the labour productivity distribution is more than nine times as productive as the firm at the 25th percentile. There is some evidence to suggest that this difference may in part be due to scale effects as we found positive associations between various measures of firm size and labour productivity. Variation in firm outcomes across the whole economy appears on average to be no less marked. Another constant across industries and cohorts is the presence of negative labour productivity outcomes, constituting nearly 13 percent of all firm-year observations on labour productivity.
On average, measured labour productivity is 35 percent of purchases per hour, although this varies substantially across firms and industries. The univariate time-series properties of sales per hour, purchases per hour and labour productivity are remarkably similar. The autocorrelations in each drop from 1 contemporaneously to about 0.6 at a 1-year lag, and then decay more gradually to around 0.2 after 9-years. Sales per hour and purchases per hour are highly correlated contemporaneously and have similar cross-autocorrelations as either univariate series. The cross-autocorrelations between sales per hour and labour productivity are positive and range from approximately 0.4 to 0.1, while the correlations between purchases per hour and labour productivity are also positive but somewhat lower.
An alternative way to examine the univariate time-series properties of sales per hour, purchases per hour and labour productivity is to calculate transition probabilities for movement of firms between quartiles of each variables respective distribution over varying lengths of time. Results for transition probabilities and autocorrelations are consistent, with the probability of a firm remaining in the same quartile of each variables distribution over time declining steadily as the interval between period’s increases. In addition, they reveal that firm entry and exit are both more prevalent for firms at the bottom of the labour productivity distribution.
In order to understand the processes driving the firm data, a simple statistical model for sales and purchases per unit of employment is developed to calibrate to the stylised empirical facts. Reassuringly, both the empirical and model results imply a large fraction of firms’ sales and purchases covary contemporaneously. However, the temporal persistence in such differences across firms is much lower. The results are consistent with 10–20 percent permanent variation across firms, and as much as 30 percent being due to purely transitory activity.
With regard to the quality of the BD and GST database, results and the strong performance of our model suggest there is some signal in the data. However, the empirical results also show substantial variation in autocorrelations across pairs of years separated by the same lag-length. Thus, although the results are somewhat encouraging with regards to the information content of the data, the year-to-year variation also demands caution. Hopefully this simple statistical model will help form the basis of economic models of firm productivity to come.
