Reading Creedy

John Creedy is really good at using complicated maths to make simple points. I'll summarise the simple points in Creedy's working paper on sugar taxes, issued earlier this month.

Section 2.1 shows that, whenever people enjoy a bundle of goods of various healthiness, and whenever people are likely to shift from one good to another if prices change, any tax on a particular unhealthy good might reduce consumption of that good while increasing consumption of other less healthy goods. Consequently, you can't just say that a soda tax would improve health - you need to show what the effects are across a broader set of consumption goods. At minimum the you'll get less than you'd hoped for in terms of effects; it's even possible to wind up getting worse health outcomes.

Sections 2.2 and 2.3 work through the maths to get an equation specifying the necessary conditions for a tax on one calorie-heavy food to yield an increase in total calories consumed. That's equation 16.

Walk it through. Food 1 is taxed, Food 2 isn't taxed. An increase in the price of Food 1, presumably through a soda tax, will increase total caloric intake whenever the inequality in Equation 16 holds. It isn't all that likely to hold, but all of these things would also limit the effectiveness of any tax in reducing calorie intake even if we don't get a full reversal from the intended effect.

The first term in the equation is the cross-price elasticity of Food 2 with respect to Food 1. How much does consumption of Food 2 go up if the price of Food 1 increases? So imagine Food 1 is soda with a soda tax and Food 2 is chocolate bars. If the price of soda goes up by 20%*, by how much does consumption of chocolate bars go up? Suppose that chocolate consumption goes up by 5% with a 10% increase in the price of soda. That cross-price elasticity would then be 0.5.

On the other side of the inequality we have another set of terms.

The first of those is the absolute value of soda's own-price elasticity. Why absolute value? Because own-price elasticity is negative (consumption drops when price goes up).

The second is the ratio of the calories in soda as compared to chocolate.

The third is the ratio of budget shares spent on soda as compared to chocolate.

And, finally, the last is the price of chocolate divided by the price of soda.

So what's needed for the soda tax to actually increase calorie intake?

• The cheaper chocolate is compared to soda, the more likely we get an increase in calorie intake;
• The more people spend on chocolate as compared to soda at the outset, the more likely that the soda tax has perverse effects;
• The more calories per unit in chocolate bars as compared to soda, the more likely we are to have perverse effects.

And even if you don't wind up in the case where the soda tax increases calorie intake, you still get less calorie reduction than you'd have expected whenever the three points above are more important. 

I love John's work, but it is pretty tough to read through it unless you know the maths. I don't think he deliberately writes these things to exclude people who can't understand the maths, but it's pretty hard for anybody who doesn't follow the maths to read. 

And so it was ... frankly bizarre ... to read this from the Public Health Blog people:

The Government has an action plan to tackle childhood obesity, but it lacks a tax on sugary drinks – a strategy for which there is good evidence.  A new Treasury Report on soft drink tax price elasticities has just emerged. It has the look of a strategically published document that if and when – during election year – certain politicians need to defend non-action on taxing sugary drinks, they can point to this Report and obfuscate.  Indeed, this New Zealand Treasury Report has already been used for this purpose in Australia. We critique this Report in this blog, with a view to preventing its misrepresentation and to encourage a more informed discussion on taxing sugary drinks. [emphasis added]

If the government wanted to push a strategic anti-sugar-tax report in an election year, it wouldn't have had John Creedy write it. Like, just look at this summary he provides of his illustrative example.

And do note that the text below the graph is about as layperson-friendly as John gets. Does this look like a political document? I wonder what has to be going on in your head if you think that John Creedy is part of some big government conspiracy to write heavily mathy things that maybe one in a thousand people can read.

The public health people then use John's equations to show that it isn't particularly likely that we get an increase in total calorie consumption with a soda tax, but that's not the main point in there. The main point in there is how the effectiveness of any soda tax drops with the combination of things listed in my three bullet point summary.

And as for any alternative theory that would have "Oh, they're writing this up so that people like Crampton can use it in arguing against sugar taxes", well, I didn't even see the point in blogging this piece until they mentioned it. It seemed way too impenetrable even to try blogging about. I'd be a bit surprised if anybody were even still reading this post by now after the maths above.

I did tweet about the report when it came out, mostly because I was exceptionally proud that The Initiative's Jenesa Jeram's work on soda taxes was cited by one of New Zealand's gods of empirical public finance (see footnote 2!).

The other fun bit in the public health people's blog post: they have a big summary of all the not-economists who agree with them about taxes, but continue to ignore Waikato University Professor of Economics John Gibson's work.

But that doesn't mean you have to ignore it. He's giving a talk in Auckland on it that I'd be attending if I were in Auckland. He shows how the estimates of the effects of soda taxes in Mexico are overestimated because consumers shifted to cheaper sodas and, consequently, reduced their soda consumption by maybe a third as much as is often suggested.

And note that John's work on soda taxes is funded through the Royal Society's Marsden Fund, so it's harder for the public health types to simply dismiss on the basis of its funding.

Update: On further thought, it seems a bit odd that Boyd Swinburn is one of the authors on here. The first paragraph implies that John Creedy's work was politically swayed. For a guy who is suing Whaleoil for defamation...


* Note: only an idiot would think that this does not apply to excise just because I used the percent sign and excise is done per unit of whatever rather than in percent terms. Elasticities are just done in terms of percentages. You can turn any excise into a percentage change around different price thresholds to get point elasticities. The effect of any per-unit excise depends on price elasticity. You can probably judge whether somebody gets to count as an economist based on whether they get this. Getting it isn't sufficient for being an economist, but it's necessary.

Inequality crisis?

Consumption inequality in New Zealand is down. Not just down on the mid-1990s post-reform peak, but also down relative to 1984.

That's the conclusion out of new work by Ball and Creedy at the Treasury. I cover it over at The Initiative's Sandpit blog. But here's the key figure.

The dashed “Market” line traces Gini inequality in market earnings over the period – that’s before taxes and transfers. That series rose from the late 1980s through about 1994, then levelled off before easing back to early 1990s levels.

The solid “Disposable” line tracks Gini inequality in disposable incomes – that’s after tax and transfer. This measure rose from 1988 through to about 1994 then was basically flat. Note that the spike at 2001, and again around 2010, coincide with tax changes that encouraged income shifting from one year to another, generating the hump.

The dashed “Consumption” line is the one that’s particularly interesting. It measures inequality in real consumption. That measure rose a bit from the late 80s, plateaued through the mid-90s, and has eased off since then. Current inequality in consumption is lower than it was before the 80s reforms.

I doubt that data will have much effect on media frenzies around inequality. But at least you and I know better.

GST confusion

In last week's NZ Initiative "Insights" newsletter, I'd hit on public misunderstandings around GST. People think taking GST off food would be strongly progressive, because poor people spend a greater fraction of their income on food, but richer cohorts get a much larger fraction of the total benefit because they spend more in total on food. If you want to help poorer people, run the redistribution directly rather than taking GST off food.

I have never been a fan of the old prayer wishing confusion upon one’s opponents. In a real war, your enemy’s confusion helps. But in policy battles, it rather seems to me that that confusion hurts everybody.

Take GST. New Zealand is blessed with what is about the world’s cleanest value-added tax. Australia’s GST is in dire need of modernisation – their tax exemption regime around food, for one, makes ridiculous and arcane distinctions between bread and crackers and around just what gets to count as a pizza, as noted by the Australian Broadcasting Corporation this week.

Nevertheless, it is not hard to find local advocates of exempting ‘healthy’ food from GST to change peoples’ diets, or for exempting food entirely to help poorer people. Both proposals are hopelessly confused: they are very costly ways to fail to achieve the desired objectives.

To start with, so long as richer people spend more money on food than do poorer people, exempting food from GST does more to help richer people than it does to help poorer people. If your goal is to help poorer families be able to afford more food, policies that reduce the cost of housing leave more space in the budget – but we will come to that later. Food exemptions from GST are a very expensive way of helping poorer people as compared to just using our existing income transfer programmes – or making jobs easier to get.

Further, exemption regimes make a mess of GST accounting. If you think that we should tax people until they eat the way you want them to eat, it is better done with an excise regime than by wrecking GST. We will be taking on the case for and against food taxes later in the year.

I hadn't known it at the time, but John Creedy and co-authors have run the numbers on this one. Their abstract, in a forthcoming NZEP piece:

This paper investigates the welfare effects on New Zealand households of zero-rating food in a goods and services tax (GST). The detailed effects, for a range of household types, are investigated using Household Economic Survey data. Demand responses to consumer price changes are estimated and welfare changes, in terms of equivalent variations, are obtained. Comparisons are also made across clusters, consisting of groups of households with similar characteristics. A tax change is found to produce a very small amount of progressivity in the GST. Redistribution is from households without children and with high total expenditure to households with children and low total expenditure, and towards older households.

You get far more progressivity, if that's what you want, by transferring more money to poor people. Their bottom line?

The analysis supports earlier studies suggesting that the use of zero-rating in an indirect tax structure provides a poor redistributive instrument compared with direct taxes and transfers

Good news and better news

Treasury today released two bits of good news.

There has been a lot of handwringing over the last decade or more about savings rates in New Zealand. I've never been sure that it's all that much of a problem except inasmuch as it would make it hard for a later government either to raise the age of superannuation eligibility or to cut superannuation rates in a hurry if nobody got around to slowly raising the age of eligibility on a fixed future schedule.

Emma Gordon, Grant Scobie, and Yongjoon Paek find household savings are higher than we had previously thought, and even more so when we consider the savings held in the NZ Superannuation Fund. They also find that we've overstated the current account deficit by a couple of percentage points.

Upshot:

The consequence of these is that some of the very extreme levels of household dissaving seen between 2004 and 2009 have been revised such that the current estimates of negative saving by households from the household income and outlay account are very much more modest. Over this period the annual average change was an improvement in the saving rate of households of over 7 percentage points of disposable income. These revisions underscore the importance for the policy debate to be grounded in solid evidence, and for full cognizance of the limitations of the underlying data.

The second bit of good news: the long term projections aren't as bad as we might have thought. John Creedy and Kathleen Makale have built some probabilistic projections on social spending. The baseline case is below.

Those are mean estimates with a lot of uncertainty, as you can see from the relatively wide bands around the mean in the figure above.

If we can manage to increase the age of superannuation eligibility to 70 and keep people in the labour force for longer, social expenditure as a fraction of GDP will max out at around 24% of GDP in 2040 rather than around 29%.

I'm not sure how much of the work in the mean projections around less growth in social expenditure comes from increasing the age of superannuation eligibility and how much comes from assuming people will work longer rather than self-fund retirement before Super kicks in (in combination with pushing back some age-related health care expenditures). And all the central tendency numbers seem to depend on maintaining recent relatively higher immigration rates, which likely in turn depends on fixing land use planning so that Green-style xenophibia-via-housing-prices doesn't get entrenched. And they also might depend on an assumption that mortality rates only decline through the next 15 years and are flat thereafter: a Superannuation age of 67 or 70 could be a lot more costly if retirement duration keeps lengthening. If we set the age of superannuation eligibility to increase to 70 over a medium term, then automatically increase it with life expectancy to give a fixed expected retirement duration, that would help a lot. And it's still not good: those are the kinds of numbers I'd like to be seeing for total government expenditure rather than just social expenditure, though that's more of an aesthetic preference. But I was scared it was going to be worse. So that's the better news.