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Toward a Model of Firm Productivity Dynamics - WP 06/11

1  Introduction

Firm unit record data have proved to be a rich source of information for understanding how firm dynamics contribute to industry-level and economy-wide productivity growth. The survey by Bartelsman and Doms (2000) emphasised in particular the importance of the development of longitudinal micro-level data sets which have enabled documentation of micro-level productivity growth, examination of the factors associated with firm productivity and more rigorous exploration of causal relationships. The aims of this paper are to describe a longitudinal New Zealand firm unit record dataset compiled from various sources including goods and services taxation data, to explore the properties of these data, to draw out some inferences about New Zealand firm productivity, and to use the revealed statistical properties to guide the specification of a model of firm productivity dynamics.

Some of the inferences about New Zealand firm productivity performance that can be drawn from the firm unit record data analysed in this paper are the degree of heterogeneity of productivity performance across firms, the degree of persistence in firm productivity and the extent to which firms move over time within the distribution of firm productivity. The paper explores some relationships between firm entry, exit, size and productivity performance. It also calibrates a simple stylised statistical error components model that is (broadly) consistent with the stylised facts pertaining to the time series properties of the firm unit record data which will help inform the development of richer models of New Zealand firm productivity.

One approach to modelling firm productivity dynamics now commonly applied to longitudinal firm databases is to use techniques suggested by Griliches and Regev (1995) and by Foster, Haltiwanger and Krizan (1998). These techniques decompose total productivity growth over time into contributions from within-firm productivity growth, changes in market share, and contributions from exiting and entering firms. A common finding from this stream of research is that within-firm productivity growth tends to dominate the contributions of firm entry and exit to aggregate productivity growth. For example, Baily, Bartlesman and Haltiwanger (1996) conclude that the within-firm component accounted for almost half of the growth of total factor productivity for US manufacturing establishments during the 1980s while net entry accounted for about one quarter of that growth. The OECD (2004) found that for the manufacturing sectors of several OECD economies during the years 1987 to 1997, within firm productivity growth accounted for the bulk of overall labour productivity growth, the contribution from changes in market share varied across countries and time but was typically small, and that the net contribution from entry and exit accounted for between 20 and 40 percent of labour productivity growth. Broadly similar conclusions were drawn for New Zealand in a recent study by Law and McLellan (2005) which used exactly the same firm unit record database that will be compiled and analysed in this paper.

Understanding the dynamics of within-firm productivity growth is therefore a crucial step toward understanding industry and aggregate productivity growth. The aim of this paper is to develop an empirical model that sheds some light on within-firm productivity growth. Recognising the potential insights documented for example by Bartelsman and Doms (2000), the approach in this paper is to create a longitudinal firm unit record database to analyse within-firm productivity growth. This longitudinal database is developed from Statistics New Zealand’s Business Demography (BD) and Goods and Services Tax (GST) data. The database is used to derive a measure of firm productivity. The statistical properties of the data are then analysed and applied to specify and calibrate a model of firm productivity that matches the stylised properties of the firm unit record data.

We focus particularly on the extent to which the GST-based measure of value-added we derive from these data is a useful proxy for labour productivity. As we don’t observe a robust alternative firm-level productivity measure for comparison, we rely on inference from the time series statistical properties of the data. For example, assuming there is (some) persistent difference in true productivity across firms over time, in the extreme, if the year-to-year correlations in firm-level measured productivity are zero, this would suggest that it is dominated by “noise” and the measure is a very poor proxy for firm productivity. In the absence of an obvious metric to assess the absolute quality of the labour productivity measure, we instead use the calibrated model to interpret the variation in measured productivity.

The remainder of the paper is organised as follows. Section 2 describes the data and variable construction. Various summary measures for selected variables drawn from the dataset are presented in Section 3, while Section 4 provides some simple descriptive analysis including correlations between variables across time and transition probabilities. The revealed statistical properties of the data are then used to guide the calibration of a model of firm productivity dynamics. This model and its properties are described in Section 5 which also includes comparisons between the time-series properties of the BD and GST data and the calibrated model. The model of firm productivity is derived from an autoregressive model of firm sales and purchases that contains common and firm specific shocks. The model does a surprisingly good job of mimicking the properties of the BD and GST data. The final section summarises the key insights and provides some discussion of the implications for understanding firm productivity dynamics.


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