RDP 2025-05: How Costly are Mark-ups in Australia? The Effect of Declining Competition on Misallocation and Productivity 4. Model Calibration

Jonathan Hambur and Owen Freestone

August 2025

The model has three key parameters that bed down the amount of misallocation in the economy, and therefore the cost of mark-ups:

  1. Productivity dispersion: How different are firms in terms of their productivity? This pins down differences in firm size (or more precisely market shares).
  2. Superelasticity: How do firms' mark-ups vary with their market shares? This, together with the dispersion in size, pins down the dispersion in mark-ups.
  3. The average elasticity of demand: How willing are consumers to switch between different producers, and so how much market power do firms have (on average)? This pins down the aggregate mark-up in the economy.

To estimate the cost of mark-ups, we need to figure out reasonable values for these three parameters for the Australian economy. To do so, we calculate real-world counterparts to each using firm-level microdata from the ABS BLADE database. We then match the model to their values.

More details on the data are contained in Appendix A. But at a high level, BLADE is a large administrative database with tax data on the near universe of firms in Australia. As well as tax information on their sales, employment and expenses, it contains demographic information on their industry, firm age, and other dimensions. This information can be used to estimate firm-level outcomes, including mark-ups, but also sector-level variables, such as superelasticities and industry concentrations.

The specific metrics we use for the model calibration are:

  • The share of sales accruing to the top 5 per cent of firms in an average industry. This pins down the productivity dispersion, as it pins down the dispersion in firm sizes.
    • We calculate concentration metrics at a very detailed 4-digit ANZSIC industry level (e.g. bakery product manufacturing) and take an unweighted average across industries.
  • As in EMX, we assume the Klenow-Willis form of the Kimball aggregator. This implies that the superelasticity can be estimated using a nonlinear regression of mark-ups on market shares (see Appendix A).
    • Regressions are run for each detailed 4-digit ANZSIC industry, including firm fixed effects (and so identifying off changes in mark-ups and size). They are then aggregated across industries using industry sales weights. Estimates are the same as in Champion, Edmond and Hambur (2023).
  • The aggregate mark-up in the economy, which directly relates to the elasticity of demand.
    • We construct this both as a cost-weighted average of firm-level mark-ups and as a harmonic sales-weighted average, as suggested by EMX, using mark-up estimates from Hambur (2023).[8]

Values for each of these calibration targets are shown in Table 1. The degree of concentration increased by around 2 percentage points from the mid-2000s to the mid-2010s, while mark-ups increased by around 5 per cent. We assume the superelasticity remains unchanged due to the relatively short sample, but the sensitivity of the results to this assumption is tested in the robustness section.

Table 1: Model Calibration Targets
Baseline model
  Mark-up Concentration(a)
Top 5 per cent share		 Superelasticity
Harmonic sales-weighted Cost-weighted
Mid-2000s 1.18 1.25 68 per cent 0.13
Mid-2010s 1.25 1.33 70 per cent 0.13

Note: (a) Concentration based on unweighted average of industry-level shares.

Sources: Authors' calculations; Hambur (2023).

Table 2 shows the calibrated parameters to meet these targets. We can see that to meet the higher mark-ups in the later period, the average demand elasticity declines moderately.

Table 2: Model Parameters
Baseline model
  Harmonic sales-weighted   Cost-weighted
Pareto tail ξ Demand elasticity σ Pareto tail ξ Demand elasticity σ
Mid-2000s 5.59 9.45   4.00 7.26
Mid-2010s 4.04 7.02   3.05 6.03

Table 3 shows the other parameters in the model. For most other parameters we take them directly from EMX, as they are broadly in line with equivalent measures for Australia (e.g. the labour share of income).[9] However, we change the materials share of gross output to better align with the Australian economy.

Table 3: Other Parameters
Baseline model
Parameter Value
Discount rate β 0.96
Depreciation rate δ 0.06
Exit rate 0.04
Labour share of value added ( 1−α ) 2/3
Elasticity of labour supply 1
Elasticity of substitution between value added and materials θ 0.5
Materials share of gross output 0.47

Sources: Authors' calculations; Edmond, Midrigan and Xu (2023).

Footnotes

EMX argue that the input-weighted and harmonic sales-weighted averages should be identical. This relies on certain assumptions, including a common elasticity of output with respect to value added and wage rate, which may not actually hold in the data and mark-up estimations. [8]

The exit rate is significantly below the actual overall exit rate for the Australian economy, which tends to be around 10–15 per cent (depending if non-employing firms are included). But EMX target an employment-weighted metric – the share of employment by previously existing firms. Using ABS Counts of Australian Businesses data on exits by firm size, and taking firms to be in the middle of each employment size bucket, leads to quite a similar number to EMX. [9]