Appendix A: Data, and Mark-up and Superelasticity Estimation | RDP 2025-05: How Costly are Mark-ups in Australia? The Effect of Declining Competition on Misallocation and Productivity

RDP 2025-05: How Costly are Mark-ups in Australia? The Effect of Declining Competition on Misallocation and Productivity Appendix A: Data, and Mark-up and Superelasticity Estimation

Jonathan Hambur and Owen Freestone

August 2025

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A.1 Data

The firm-level data used in this paper come from the ABS's Business Longitudinal Analysis Data Environment (BLADE). This is a longitudinal dataset of administrative tax data matched to ABS surveys and other data for (almost) the entire population of firms in Australia.

While BLADE has data on the (near) universe of Australian firms, our analysis focuses on the non-financial market sector, given difficulty measuring outputs and inputs in these sectors. As is common in the literature we remove any firms with less than one full-time employee. Even with these exclusions the data cover a very large and representative sample of economic activity in the sectors analysed.^[16]

The data used for mark-up estimation come from firms' business income tax (BIT) forms and pay as you go (PAYG) employment forms. The former contain data on firms' sales, income and expenses, as well as on their balance sheet. The PAYG statements contain information on headcount and full-time equivalent (FTE) worker numbers, which are used as the labour input for mark-up estimation.

A.2 Mark-ups

Mark-up estimates are taken from Hambur (2023). This paper estimates mark-ups using a gross output production function, of a translog form, using the production function approach pioneered in De Loecker and Warzynski (2012).

Regarding the key data 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.
Labour input: FTE derived from PAYG statements, using the methodology laid out in (Hansell, Nguyen and Soriano 2015).
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 discussed in a number of papers, the use of industry deflators can make it difficult to identify the level or mark-ups (e.g. Bond et al 2021). That said, while the levels might be affected, the changes are unlikely to be overly affected, assuming that the production function and its estimates remain broadly constant (De Loecker and Warzynski 2012). As such, the lack of firm-level prices is unlikely to substantially affect the results on changes in the mark-ups.

A.3 Superelasticity

As in EMX, for the baseline model we use the Klenow and Willis version of the Kimball aggregator. This implies that the inverse demand function facing the firm f (q) is given by

(A1)

ϒ^{'} (q i) = \frac{\bar{σ} - 1}{\bar{σ}} \exp (\frac{1 - q_{i}^{ε / \bar{σ}}}{ε}), \bar{σ} > 1

where $\bar{σ}$ is a measure of the aggregate average demand elasticity.

The parameter $ε / \bar{σ}$ is the superelasticity of demand. It controls how demand elasticity $σ (q i)$ varies with relative size q_i. CES demand is the special case where $ε = 0$ , so demand elasticity is $σ (q i) = \bar{σ}$ , constant and independent of q_i, and hence there is no dispersion in mark-ups (at least no systematic variation).

This demand system will imply a one-to-one nonlinear relationship between the mark-up $μ_{i}$ and its sales share $ω_{i}$ that can be written

(A2)

F (μ_{i}) = a + b \ln ω_{i}, b = \frac{ε}{\bar{σ}}

where the function

(A3)

f (μ_{i}) : = \frac{1}{μ_{i}} + \ln (1 - \frac{1}{μ_{i}})

is strictly increasing and free of other parameters. So, the slope coefficient b in this relationship is the superelasticity of the demand system.

To estimate this variable we take out mark-ups estimates and transform them. We then regress them on the observed sales share $ω_{i}$ . We do so for each 4-digit detailed industry. We include firm fixed effects and so just identify off how mark-ups change as sales shares change. We then aggregate these industry-level superelasticities into division-level or aggregate superelasticities using industry sales weights.

Footnote

Hambur (2023) shows that for the non-mining, non-financial market sector, mark-ups estimates we use cover on average about 60 per cent of the sales in each constituent industry division analysed. [16]