Toward a Model of Firm Productivity Dynamics

A common finding from international research on firm productivity dynamics is that withinfirm productivity dynamics tend to dominate the effects of firm entry and exit on aggregate productivity. The aim of this paper is to explore the suitability of Statistics New Zealand's Business Demography (BD) and Goods and Services Tax (GST) data as a basis for modelling within-firm productivity dynamics. The paper first analyses and describes the cross-sectional and time-series properties of sales, purchases and a value-added measure of labour productivity. Cross-sectional results reveal a great deal of heterogeneity in average sales, purchases and labour productivity both across and within industries and cohorts. Univariate time-series properties of these variables are remarkably similar and sales and purchases are highly correlated contemporaneously. Transition probabilities are also calculated for movement of firms between quartiles of the labour productivity distribution over varying lengths of time. In order to understand the processes driving the data, a simple statistical model for sales, purchases and value-added per unit of employment is developed to calibrate to the stylised empirical facts. The model does a remarkably good job at mimicking the properties of the BD and GST data.