Analysis · Concentration
When did the market stop spreading out?
The Manufacturers page shows the Herfindahl–Hirschman index (HHI) falling from about 3,915 in FY 2009/10 and then creeping back up. This page puts intervals on the annual figures and asks when the turn happened, with an interval for the turning point itself.
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Change-point check
A broken stick through 189 months
The model is two straight lines that meet at an unknown month: HHI = a + b · month + d · (month − break)₊. The break is the month that minimises the squared error, with at least 24 months on each side. To put an interval on the break, the residuals are resampled in blocks of 20 consecutive months (a moving-block bootstrap), the break is found again in each of 1,000 resamples, and the middle 95% is reported (seed 20090701).
The residuals move slowly: their autocorrelation is 0.96 at lag 1, 0.87 at lag 3, 0.72 at lag 6 and 0.33 at lag 12. Blocks have to be long enough to keep that dependence, so the length is chosen from the residuals with Politis and White’s automatic rule (circular-block estimate, rounded) rather than a rule of thumb. Shorter blocks break the dependence up and give an interval that is too narrow; the table below shows by how much.
Manufacturer concentration over time
- Monthly HHI
- Broken-stick fit
- Break
- Dec 2015 (95% CI Aug 2015 to Jun 2016)
- HHI change per year before the break
- −224 (95% CI −247 to −201)
- HHI change per year after the break
- +36 (95% CI +24 to +49)
Annual mean HHI with 95% intervals
Percentile bootstrap over the year’s months (2,000 resamples, seed 20090701). FY 2023/24 has nine months: the manufacturer reports for October to December 2023 are missing. Most intervals are only a few index points wide, narrower than the dots; the exact values are in the table below.
HHI from CBS monthly machine counts by manufacturer (shares recomputed from the counts). The broken stick and its bootstrap are in web/src/lib/stats/segmented.ts, checked against a numpy grid search.
Reading the break
What the interval covers
Sensitivity
How much the block length matters
The same bootstrap with other block lengths. The break itself does not move; its interval widens as the blocks get long enough to carry the residuals’ autocorrelation, and settles once they do. The headline uses the automatic choice.
| Block length | Break (95% CI) | Interval width | HHI change a year, before | After |
|---|---|---|---|---|
| 6 months | Dec 2015 (Sep 2015 to Mar 2016) | 6 months | −224 (−239 to −210) | +36 (+27 to +45) |
| 12 months | Dec 2015 (Aug 2015 to Apr 2016) | 8 months | −224 (−247 to −203) | +36 (+25 to +47) |
| 20 monthsautomatic choice (used above) | Dec 2015 (Aug 2015 to Jun 2016) | 10 months | −224 (−247 to −201) | +36 (+24 to +49) |
| 24 months | Dec 2015 (Jun 2015 to May 2016) | 11 months | −224 (−250 to −201) | +36 (+22 to +49) |
1,000 resamples per row, seed 20090701, names as published. The rule of thumb n1/3 would give 6-month blocks, the first row. Block bootstraps assume the residuals are stationary; the October to December 2023 gap is treated as if the months were consecutive.
Table
Annual HHI with bootstrap intervals
Point estimates are the Manufacturers page’s figures (the mean of the monthly values). The intervals are narrow because the index moves slowly within a year; they describe month-to-month variation, not sampling error.
| Financial year | Months | HHI, names as published (95% CI) | Lineage combined (95% CI) |
|---|---|---|---|
| FY 2009/10 | 12 | 3,915 (3,868–3,960) | 3,915 (3,868–3,960) |
| FY 2010/11 | 12 | 3,583 (3,535–3,634) | 3,583 (3,535–3,634) |
| FY 2011/12 | 12 | 3,279 (3,232–3,327) | 3,279 (3,232–3,327) |
| FY 2012/13 | 12 | 3,064 (3,039–3,089) | 3,064 (3,039–3,089) |
| FY 2013/14 | 12 | 2,887 (2,863–2,913) | 2,887 (2,863–2,913) |
| FY 2014/15 | 12 | 2,740 (2,716–2,765) | 2,740 (2,716–2,765) |
| FY 2015/16 | 12 | 2,603 (2,586–2,621) | 2,603 (2,586–2,621) |
| FY 2016/17 | 12 | 2,527 (2,509–2,545) | 2,527 (2,509–2,545) |
| FY 2017/18 | 12 | 2,510 (2,505–2,515) | 2,512 (2,506–2,518) |
| FY 2018/19 | 12 | 2,592 (2,590–2,593) | 2,599 (2,598–2,601) |
| FY 2019/20 | 12 | 2,608 (2,602–2,612) | 2,617 (2,612–2,622) |
| FY 2020/21 | 12 | 2,629 (2,617–2,641) | 2,638 (2,626–2,650) |
| FY 2021/22 | 12 | 2,658 (2,647–2,670) | 2,660 (2,650–2,671) |
| FY 2022/23 | 12 | 2,728 (2,716–2,739) | 2,728 (2,716–2,739) |
| FY 2023/24 | 9 | 2,789 (2,782–2,796) | 2,789 (2,782–2,796) |
| FY 2024/25 | 12 | 2,843 (2,833–2,853) | 2,843 (2,833–2,853) |
2,000 percentile-bootstrap resamples of the months in each year, seed 20090701. Under the 2010 US merger guidelines an HHI above 2,500 counts as highly concentrated; the threshold is a reference point, not a finding about this market.