RDP 2023-03: Doing Less, with Less: Capital Misallocation, Investment and the Productivity Slowdown in Australia Appendix A: Data and Sample Statistics

As discussed in the paper, we use data from the ABS BLADE database. The particular data come from firms' business income tax forms and PAYG employment forms.

Regarding the key variables:

• Gross output: measured as firm income. This will include some income not directly related to production, such as interest. However, for most firms this item is small.
• Labour expense: labour costs plus superannuation expenses.
• Fixed costs: rental and leasing expenses, bad debts, interest, royalties, external labour and contractors.
• Intermediate inputs: total expenses less labour, depreciation and fixed costs.
• Value-added: gross output less intermediate inputs.
• Labour input: FTE derived from PAYG statements, using the methodology laid out in Hansell et al (2015).
• Wage rate: labour expense divided by FTE.
• Capital: book value of non-current assets.

All of these metrics apart from FTE are measured in nominal terms. To construct real measures for the inputs into the production functions, we deflate using division-level output, intermediate input and capital deflators. The wage rate is deflated using the output deflator.

As well as our main capital stock measure, we also construct a PIM. To construct this metric we use the following law of motion:

where $K_t^{PIM}$ is the real PIM stock in time t, I_t+1 is real investment in t + 1 deflated using the gross fixed capital formation deflator, ${\delta }_{t+1}$ is depreciation in t + 1 deflated using the previous capital stock deflator, and D_t+1 is disposals in t + 1 deflated using the lagged capital stock deflator.

To use a PIM we require a starting value. Our preferred starting value is the firm's reported capital stock in the first year we observe the firm. We also tried assuming the stock was zero in the previous year, and building the stock based on flows. Both lead to similar results.

The PIM approach is not our preferred approach for two reasons. First, PIM can be sensitive to the starting value, particularly in short samples (though that does not appear to be a substantial issue here). The second is that disposals are reported at the cash value of the sale, not the book value. While some data are available on any taxable gain/loss on the sale, which would allow us to get back to the book value, these are not provided for the entire sample.

As noted, we focus on the market sector, and so exclude the Health, Education, and Public Administration divisions. Government plays a large role in these divisions, and capital reallocation may be heavily influenced by public entities. We also exclude the Finance division, given conceptual difficulties in measuring output in this sector (e.g. La Cava 2019).

We exclude all non-employing firms, given these firms will have undefined (log) labour inputs and costs. We choose to exclude all firms with less than one FTE as is common in the literature, as they introduce a large amount of noise into the estimation of MFP. We exclude all sole proprietors, as they do not report information on their balance sheets, and so on their capital stock. Finally, we exclude industries that have very few firms due to difficulty in estimating production functions with small samples. This mainly affects the Mining and Utilities divisions.

Even with these exclusions, we capture a very large proportion of the non-mining non-finance sector (see Hambur (forthcoming)). That said, our sample is slightly skewed towards larger and older firms, compared to the full population (Table A1).