Like many policy issues in Australia, the public debate and media coverage on the relationship between government payments and spending at electronic gaming machines or ‘pokies’ is sensationalist and exaggerated.

Much of it can accurately be described as fearmongering. Tabloid coverage following the distribution of the Carbon Tax compensation cheques in May and June 2012 was no exception. Headlines from 18 July in Fairfax publications, the Sydney Morning Herald and The Age read “Pokies swallow carbon tax compo”.

A similar headline,“Gambled away: pokies swallow carbon tax compo”, appeared in the Australian Financial Review on the same day. The Brisbane Times also reported that poker machines were ‘soaking up’ the carbon tax cash ‘handouts’. No matter what you read the message was identical: Australians blew their carbon tax compensation cheques at the pokies.

In an interview with ABC’s Lateline, anti-pokies crusader Nick Xenophon described the cheques as an unjust enrichment to pokies operators and referred to them as an “electoral bribe”. He then suggested in-kind rebates are more appropriate policy instruments than cash transfers.

The implication was that Australians didn’t make appropriate consumption decisions and the government should have placed limits on their spending discretion. The problem is that Xenophon and the media were wrong and the public was misled: the carbon tax cheques were not “swallowed” by poker machines under any reasonable use of the word.

The methodology used by pundits and the media – calculating the percentage change in gambling losses between May 2011 and May 2012 – is inappropriate for at least three reasons. The first, and probably the most obvious, is that correlation doesn’t imply causality. A multitude of extraneous factors can explain year-on-year changes in gambling at poker machines.

Second, the method fails to account for time trends in spending at electronic gaming machines (EGMs). The overall trend for Victoria has been a decline since 2009. Moreover, many areas of Victoria have predictable seasonality patterns. The Surf Coast, for example, sees the majority of gambling in the summer months.

The third problem is selection bias, even if the 7% year-on-year increase in Bendigo was the direct effect of the carbon tax cheques, this doesn’t imply a widespread “swallowing” across the entire state as suggested by media coverage.

Maroondah, which has higher rates of spending than Bendigo, recorded a year on year decrease of 7%. On the lower end of the spectrum, Bass Coast saw a 14% decrease in May 2012. Should we conclude from this that the carbon tax cheques decreased spending at EGMs?

Figure 1 shows a box plot of “Net Expenditure” – the industry term for gambling losses – per EGM across all Local Government Areas (LGAs) in Victoria over the period July 2004 to June 2012. The data come from the Victorian Commission for Gambling and Liquor Regulation (VCGLR), which has kept track of spending at poker machines in Victoria since 1992.

A casual glance at Figure 1 reveals that some LGAs are clearly more consistent than others. For the 2011-12 financial year, the average net expenditure per EGM in Whittlesea – home to 621 machines – was $11,087 per month.

The yearly total at June 2012 was more than $1 million or roughly 4% of the $2.6 billion recorded in Victoria. At roughly $600 per adult, it’s no surprise that Australia has the highest per capita EGM expenditure in the world. In absolute terms, spending at EGMs in Australia is about the same as Las Vegas and Atlantic City combined.

In a paper to be released in the 2013 Melbourne Institute Working Paper Series, Hielke Buddelmeyer and I show there was no significant increase in spending at poker machines in May or June 2012.

There was, however, a clear and measurable increase in spending at EGMs following the 2008-09 stimulus cheques. We have made our methods and data publicly available on Dataverse so that others can replicate our findings.

Figure 2 shows the estimated monthly anomalies in net expenditure for each of the 96 months in the 2004-2012 period we examined. The largest anomaly, estimated to fall within $669 to $1011 per EGM, occurred when the December 2008 stimulus cheques were paid to Australian households. By contrast, estimated monthly anomalies of –$374 to $14 and –$200 to $187 per EGM occurred when the carbon tax cheques were distributed in May and June 2012.

Although this suggests Victorians spent less than expected at EMGs during the carbon tax compensation months, the uncertainties in the May and June 2012 estimates are too large to place a great deal of confidence in them. Because the signs for these estimates fall on both sides of zero any inference risks what is sometimes called a “Type S error”. The true anomalies could have been negative, or slightly positive.

Nevertheless, the May and June 2012 anomalies are hardly synonymous with a swallowing. Because gambling is a normal good – consumption increases with income – some portion of any windfall income or “handouts” provided by the government will find its way into poker machines.

For the same reason economists expect an increase in retail sales after a boost to household income any increase in gambling is unsurprising. The relatively insignificant spending estimates for the carbon tax months were unexpected. There are two likely explanations for this.

First, the carbon tax compensation cheques were much smaller than the 2008-2009 fiscal stimulus cheques. As an exercise, assume a person’s marginal propensity to gamble at EMGs is constant, say 0.20. Then she would spend 20 cents of every additional dollar of income at EGMs. The total amount distributed by the carbon tax compensation cheques was about $325 million and Victoria’s share of this was about $79 million. Using the assumption that everyone in Victoria has a 0.20 marginal propensity to gamble implies $15.8 million extra spent at EGMs. This estimate is much larger if we consider the stimulus cheques.

We estimated Victoria’s share of the December 2008 fiscal stimulus was $2.2 billion. Under the same assumptions this implies an increase in EGM spending of $440 million. Of course, we know that the hypothetical marginal propensity to gamble of 0.20 cannot be applied to the entire population as surveys suggest only 20% of Victorian adults frequent EGMs.

The point is that the sheer size of the December 2008 cheques makes any relationship between gambling and windfall income easier to measure, as illustrated by Figure 2. On the whole, we estimated that about $22.5 million, or 1%, of the December 2008 stimulus was lost at EGMs in Victoria. This is clearly a substantial amount of money but it only accounts for a small fraction of the December 2008 stimulus.

The second explanation lies in the fact that the carbon tax cheques were described as a rebate to offset a forthcoming tax whereas the stimulus cheques were framed as a bonus.

Behavioural economists and psychologists have demonstrated in a number of experiments that people are more likely to spend and spending rates are much higher when windfall income is framed as a bonus rather than a rebate.

If we accept that these experimental results are generalisable then it is no surprise that the stimulus cheques created substantial anomalies in net expenditure and the carbon tax cheques did not.

Whatever the moral concerns about gambling may be, it is simply not true that the carbon tax cheques or the stimulus cheques were “swallowed” by poker machines. A relatively small amount of any form of windfall income will always end up in EGMs.

It appears that enough of the stimulus money made its way into poker machines to create an observable anomaly in EGM expenditure but the same cannot be said for the carbon tax cheques. Of course, the relevant public policy issue is how problem gamblers – a very small number of Australians – are affected by EGMs.

The most reliable estimates available come from the Productivity Commission and suggest that 80,000 to 160,000 or 0.5% to 1% of Australian adults have significant gambling problems.

This includes about 15% (or 95,000) of Australia’s 600,000 regular EGM players. For the same reason that a few crazy politicians doesn’t necessitate mental health screening as a prerequisite to holding office, we shouldn’t require all government spending to be in the form of in-kind transfers to prevent some money ending up in poker machines.