1351.0.55.164 - Research Paper: Approaches to Analysing Micro-Drivers of Aggregate Productivity, March 2019  
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Approaches to estimate the firm contributions to aggregate productivity

This research estimates the contribution to productivity growth in Australia in the period 2002 – 2013 of:

    firm entry and exit
    firms within industries and
    firms between industries.
We compare two different decomposition approaches to estimate the firm contributions to aggregate productivity. We find that firm entry and exit are by far the largest contributors to productivity growth across all industries.

Chart 1 shows that, in general, firm exit contributes positively to productivity growth, whereas firm entry contributes negatively. The two approaches provide similar results but the approach of Melitz and Polanec (2015) uses appropriate benchmarks for calculating the contributions from the entering and exiting firms.

Chart 1 Comparison of decomposition approaches

Image: Comparison of decomposition approaches

Instrumental variable, preconditioned conjugate gradient and grouping algorithms

This research applies an instrumental variable regression to reduce the bias in estimating firm productivity. We derive the instrumental variable from an experimental linked dataset of 10 million workers across 1.5 million firms. It is not feasible to perform calculations on a matrix with 130 million rows and 11.5 million columns. Therefore, we use a preconditioned conjugate gradient algorithm to solve a large sparse matrix and a grouping algorithm to identify unique solutions.

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