When is public spending worth it?
Understanding the shadow cost of public funds
In my most recent post for Progress Ireland, I wrote about the economic incidence of corporation tax. This post builds on that one: you don’t have to read it first, but it will help with some of the economic intuitions.1
The previous blog aimed to help our understanding of questions like: when corporation tax is increased, what fraction of that economic burden is borne by workers, as compared with shareholders or consumers? But that does not tell us the true cost of tax. And to make an informed judgement about when public spending is justified, we need to understand the costs.
The cost of €1 in taxes is almost always more than €1. This is primarily because of deadweight loss: tax shifts people’s behaviour away from what they would have chosen to do in the absence of the tax.2 Perhaps they work less in the presence of an income tax, or move less often when they have to pay stamp duty on a house. Another way to think about this is that there is a set of mutually beneficial trades that no longer occur. The deadweight loss of tax can be visualised beautifully on a supply and demand diagram, as the area of a Harberger triangle:3
The face value of a tax, combined with the economic distortion it causes, makes up the marginal cost of public funds (MCPF). That is also known as the shadow cost of public funds. The reason why MCPF is so important is that it determines which investments are worthwhile for a government to make. If a project would return 105 per cent of its initial investment, then even in an ideal world, the state shouldn’t pursue it; the welfare loss due to raising the tax would be larger than the benefit. But what is the breakeven point? Should we only invest in projects whose benefits exceed 1.2 times the face value costs? 1.5? Is this even the right way of thinking about it?
When someone pays tax, it shifts the distribution of what they consume, not just the amount. This is called the income effect; it reflects the ways that simply being poorer affects behaviour. In public finance, the income effect is implemented in a particular way that is usually assumed to be small or zero, especially for prime-age workers, but there is no consensus about whether that is justified. It’s extremely messy to work out whether or how we should adjust for income effects in the calculation of marginal cost of public funds. This is an active area of debate that we’ll put to the side, but I’ll share some details in a footnote.4
Oliver Wendell Holmes famously wrote that taxes “are what we pay for civilized society”. But the benefits from taxes need to justify whatever costs there are from raising them. Those effects are quite subtle to understand, and, in my experience, are usually underestimated.
So, buckle your seatbelts, because you are about to learn a lot about the marginal cost of public funds. We’ll work our way up to calculating a value of it for the Irish economy. But before we get to that, we’ll need to understand a few related concepts. Here’s what’s in store:
The elasticity of taxable income
The elasticity of taxable income asks: if the net-of-tax rate increases by 1 per cent, by what per cent does the amount of taxable income grow?
The net-of-tax rate is one minus the tax rate. This is confusing at first, but it simplifies matters greatly to think in terms of ‘net-of-tax’, instead of tax. If the marginal rate of income tax is 40 per cent, then the net-of-tax rate is 60 per cent. It’s this 60 per cent that provides the incentive for workers to continue working.
This figure is usually going to be less than one because, even though increasing the rate will subject more income to tax, taxes always dissuade the activity in question to some extent. If you tax labour, there will be somewhat fewer hours of work to tax. If you tax investment, there will be somewhat fewer investments to tax. Hopefully, you will be able to get away with taxes that only change people’s behaviour a small amount, compared to the world without the tax.
When we tax negative externalities, you may think of the change in behaviour induced by a tax as a good in itself. When pollution is taxed according to the externality it imposes on others, the deadweight loss is actually negative, which is why MCPF can, in principle, be smaller than one. However, this is a special case, and only taxing externalities would raise nowhere near enough money to finance a modern government.
In a celebrated paper by Martin Feldstein in 1999, he showed that, under certain assumptions, the elasticity of taxable income is a ‘sufficient statistic’ for the welfare costs of taxation. This means it tells you enough to calculate the aggregate deadweight loss of a marginal change in taxation. This really opened up the field of public finance, because it means that we don’t need to work out every different way in which people can adjust their behaviour, which seems intractable.
There is only one proper estimate for the elasticity of taxable income in Ireland. It comes from a paper from 2018 from Acheson, Stanley, Kennedy, and Morgenroth.5 Their data is unusually high-quality: it covers the period from 2004 to 2015, and the full spectrum of the income distribution. They’re also able to differentiate across a wider range of characteristics than most papers in this area, including age, employment and marital status. Even just re-running their analysis with more recent data would be a great service, but that data is not publicly available.
Their headline estimate is 0.168. When the net-of-tax rate goes up by 1 per cent, taxable income increases by about 0.17 per cent. An ETI of zero would correspond to workers making no adjustments in response to taxation.
This is on the low end by international standards.6 It basically says that the Irish government can get away with increasing taxes without people changing their behaviour much. The paper speculates about whether there are Ireland-specific factors that explain this.
The ETI is 0.145 for pay-as-you-earn (PAYE) taxpayers, and 0.363 for self-assessed taxpayers. This is in line with the conventional wisdom that self-employed people adjust their behaviour more in response to tax than do employees. There is also a stark difference by income levels: high-income taxpayers are exceptionally responsive to the tax rates, while low-income households are relatively unresponsive.
Among individuals who earn more than €100,000, the elasticity of taxable income is 3.5, albeit with a large standard error. This is difficult to interpret. Raj Chetty in 2009 argued that the elasticity of taxable income is a sufficient statistic for welfare only under specific conditions. When the elasticity reflects pure substitution between work and leisure, then Feldstein’s argument works.7 But we also know from a large body of international evidence that rich people respond to higher taxes overwhelmingly by restructuring their finances to avoid that tax, rather than by working fewer hours.8 Most of this is entirely legal and individually rational tax planning.
Suppose that a higher income tax causes a high earner to switch €10,000 more of her compensation from cash to shares compared to what she otherwise would have preferred. There is some welfare loss in that, but it’s presumably not terribly large.
Any elasticity is relative to a timescale. Acheson et al.’s calculation is medium-run: their panel data is divided into chunks of three years. This follows most of the literature since Feldstein: it’s thought to be long enough to avoid over-interpreting the significance of between-year income shifting, but long enough to see real behavioural adjustment.9 Some people (including Saez et al.) make arguments about why the elasticity of taxable income should be larger in the long run, but the magnitude of the effect has never been credibly estimated.
In one of my favourite Beatles songs, George Harrison sings “one for you, nineteen for me”, satirising the 95 per cent top rate of tax under Harold Wilson. The elasticity of taxable income for top British earners at that time was astronomical: the increases caused a large amount of substitution whereby compensation might be paid in the form of company cars, private school tuition, or other employee benefits. Naturally enough, there have always been more such avenues for tax minimisation open to higher earners.
In the Irish case, the elephant in the room is that the most significant way people can adjust their behaviour in response to government policy is by emigrating. As far as I know, no one has really studied this for Ireland, despite the fact that the international literature on migration suggests that elite human capital is quite mobile in response to taxes.
In any case, Acheson et al. only look at the distortions due to income tax. Their justification is that, as you make more in Ireland, income taxes are responsible for the vast majority of the change in the marginal rate that you pay. Most government revenue doesn’t come from income tax, but most of the increase in the rate individuals pay is from income tax. Without more data, this is a bit handwavy, and is probably the weakest section of the paper.
From the perspective of an individual paying taxes, the next most important are Pay Related Social Insurance (PRSI) and universal social charge (USC). PRSI is what Americans call a payroll tax, namely a tax on employing individuals. USC is another form of income tax, which is administered separately for complicated historical reasons. The top rate of tax on income in Ireland is 40 per cent, while PRSI is 15.45 per cent, and USC is 8 per cent.10 However, insofar as the burden of them is paid by workers – and we don’t know how much of it is! – we also need to include corporation tax, carbon tax, VAT, and every other kind of tax.
One way of thinking about tax is that it produces a gap between what consumers pay and what producers receive. This is called the tax wedge. A perfect estimate for the elasticity of taxable income would include the entire tax wedge.
All of which is to say that only looking at income tax significantly understates the marginal rate in Ireland. It’s unclear whether this implies that the true ETI is higher or lower than what the authors estimate, but we’ll get to that in the next section.
The real reason why papers in this literature often look only at income tax is the sheer messiness of linking up all the data. Income tax, PRSI, and USC all apply to subtly different sets of individuals, and calculating a comprehensive marginal rate for individuals would be a major research project in itself.
In a canonical paper by Emmanuel Saez, Joel Slemrod, and Seth Giertz from 2012, economists estimated that ETI was somewhere between 0.12 and 0.4, with the sample heavily biased toward America. When you read that paper, you get a sense for why, even when you have all the data, there are many theoretical assumptions that go into calculating this number. Working out the welfare losses from taxation is not a theory-free exercise.
There’s a good line in A Brief History of Time, where Stephen Hawking writes that his publisher told him that, for every equation included in the book, sales would fall by half. He said that this was still worth it, in order to expose his readers to the beauty of:
Unfortunately, Irish fiscal policy does not reveal as much about the structure of the universe as special relativity. But, like Einstein’s energy-mass equivalency, there’s another deep and profound equivalency here. If we assume there is no income effect, then the elasticity of taxable income accounts for all deadweight loss, which, when added to the face value of the tax, gives us the marginal cost of public funds. If you use some basic calculus to solve first-order conditions and apply a classic result called the envelope theorem, you can state this in equation form like this:
Where e is the ETI and 𝜏 is the top marginal rate of taxation.
From this, in principle, we can calculate the Irish marginal cost of public funds from the ETI value from Acheson et al. However, there isn’t just one tax rate. When the government raises an additional €1 billion, it will do so from a variety of taxes. Even within a single tax, it will be paid at a variety of rates. Even if we knew every tax and every rate paid by every individual, finding the appropriate tax rate to plug into Feldstein’s equation is not as simple as taking a weighted average across all different types of taxes. For one thing, it’s not clear how you should weight those averages. Acheson et al. average across taxable income, but you could also average across all income, or population, or government revenue. An explicit choice about this is rarely defended, despite the fact that it will produce different answers.
Finding a comprehensive “marginal rate of tax” for an economy as a whole is ridiculously complicated and arguably completely intractable.
The authors thus use a modified version of the Feldstein framework from Saez, Slemrod, and Giertz. This makes some stronger assumptions than Feldstein, but in return, it allows you to calculate MCPF using just ETI, the top rate of income tax, and a ‘Pareto parameter’ ɑ. This last number describes the shape of the distribution of upper incomes.11 Their resulting relationship looks like this:
Using this formula, the authors find an implied MCPF for Ireland of 1.35. A euro in tax costs society €1.35 in welfare: €1 of redistribution, plus €0.35 in deadweight loss.
The number is very approximate. To take just one source of uncertainty, Saez’s formula assumes that upper incomes are approximately distributed according to a power law. To the best of my knowledge, no one has rigorously checked whether the upper end of Irish incomes is distributed according to a power law, or what exponent best describes that relationship.
Public finance is a slippery area. And, maddeningly, it is made more complicated than it needs to be because the terminology is completely non-standardised. You’ll sometimes hear about the ‘social opportunity cost of exchequer funds’ (SOCEF), which is just MCPF minus one. The term ‘excess burden’ is occasionally used instead of deadweight loss. The Irish documents use the term Shadow Price of Public Funds (SPPF) for what I’ve been calling the marginal cost of public funds, and Saez et al. call it the ‘marginal efficiency cost of funds’.
That was all quite technical, and don’t worry if you didn’t follow all the details. The point is, we have an estimate for Ireland’s marginal cost of public funds: 1.35. Is that high? Low? Is this number actually used for anything?
In the next section, I’ll respond to a criticism of the methodologies used for calculating MCPF, which argues that they produce numbers that are systematically too low. I find these criticisms quite persuasive in the case of Britain, but for Ireland, the critique is weaker.
Is the marginal cost of public funds underestimated?
The methodology that was used to arrive at Ireland’s marginal cost of public funds only included income tax. There are about a dozen main taxes in Ireland, and then a long tail of dozens of more niche ones that few people have even heard of. All of them create some distortion, and ideally, we would account for them all. You might think that 1.35 is a highly conservative lower bound on MCPF, but it’s far more complicated than that.
The elasticity of taxable income is a measure of how much behavioural response there is per unit of tax, so including more taxes in your analysis could decrease the estimate, if changes in income tax produce a greater response than average. There is a well-known literature about which kinds of tax produce the biggest behavioural responses, which generally concludes that income tax is quite salient. And broadly speaking, income tax is also around the middle of the pack when it comes to the amount of distortion created per euro raised.
Duncan McClements recently published a fantastic blog post in which he dug into the methodologies used to calculate MCPF. His argument rests on the idea that most of the existing estimates for MCPF have too restrictive a notion of what should count as the marginal tax rate. In the UK, many estimates for MCPF only account for two types of tax: income tax and National Insurance.12 Often, this is a matter of necessity due to data availability.
There are two biases here, and they point in opposite directions:
By including more taxes in the calculation of MCPF, the marginal rate 𝜏 is higher.
By including more taxes, the elasticity goes down, if the new taxes induce less of a behavioural response on average.
Whether MCPF goes up or down when we consider more taxes depends on whether (1) or (2) grows more quickly. Duncan has good reasons for thinking that (1) dominates (2) in the case of the UK. The marginal rate 𝜏 in Britain is very high when you consider benefit tapers, ie, that as people make more money, they are de facto taxed in the form of losing access to government services. 𝜏 enters the Saez formula as 𝜏/(1 - 𝜏), which is a convex function. That means that, as 𝜏 gets larger, MCPF grows more quickly.
This means that methodologies that use only a few type(s) of tax will be more likely to underestimate MCPF for high-tax countries than for low-tax countries. We don’t have ETI estimates for each individual tax, so in order to get a welfare estimate, Duncan needs to assume the ETI is similar for all types of tax. This is a strong assumption, but he tries to correct for it by using ETI estimates on the more conservative end.
Since he’s assuming constant elasticity, the inclusion of more taxes will necessarily raise the MCPF estimate. When he includes benefit tapers, the apprenticeship levy, corporation tax, dividend tax, stamp duty, VAT, and a smattering of other taxes, his headline conclusion is that the UK’s MCPF is approximately 2.0. This is in stark contrast to the most commonly used estimate from Kleven and Kreiner of 1.26.13
All of this, by necessity, what Seán Keyes calls a “finger in the air job”.
But if he’s right, it would represent a radical shift in the way that the UK government does cost-benefit analysis. Many projects, including new hospital construction, building affordable housing, and installing smart meters, don’t come anywhere near a two-to-one ratio of benefits to costs. Probably few government investments clear so high a bar.
Duncan and I plugged in Irish numbers to his model, and got an MCPF of 1.75. This is not as bad as the UK, but it’s still huge! Similarly, if this were taken seriously for cost-benefit analysis, it would mean that the state ought to cancel a large swathe of its planned investments, including DART+ and MetroLink, for not justifying the distortionary effects of taxation.
The main reason why I don’t believe the true number is quite this high is because of how many assumptions one has to make to include so many taxes. There are many researcher degrees of freedom.
You might think that we are underestimating MCPF when 𝜏 is high because the Saez formula is convex in 𝜏. But recall that, in order to make things tractable, Saez has a model that only looks at the marginal rate of taxes on income. By plugging in extra taxes like corporation tax and stamp duty into the same formula, Duncan has to convert all taxes into an equivalent income tax. My previous post gave some intuitions for why doing this kind of thing is extremely complicated and speculative. Like everything he writes, Duncan’s analysis is terrifically entertaining, but I get off the train a few stops before he does.
Nobody has actually worked out what Ireland’s de facto top marginal tax rate is when you account for benefit tapers, such as losing your medical card at higher incomes. It would be an excellent summer research project. But, in the final analysis, my guess is that Ireland’s top marginal rate is somewhat higher than Britain’s. The British tax system has bizarre cliff edges at different income levels that make it hard to say for sure. We at least have fewer of those.
My anecdotal impression is that, over pints in the pub after a tax conference, most economists think that the level of distortion caused by tax is somewhat larger than the headline numbers. And I’m inclined to agree with them. Approaches that consider a more comprehensive set of taxes than the Saez methodology tend to find higher numbers.
Before we turn to how these numbers are used in practice, I want to look at one final consideration: whether, to make any of this work, we need to understand how distortions from tax change over the business cycle.
Taxes are more costly in good times than bad
There is a clever way to extract information about how responsive individuals are to changes in tax by looking at “bunching”, or the degree to which incomes suspiciously cluster just below thresholds for additional taxation. For example, if an individual loses access to their medical card at €30,000, we would expect a disproportionate number of people to earn close to €29,999. Solving some first-order conditions from a different Emmanuel Saez paper, you can work backwards from the degree of this “bunching” to the elasticity of taxable income.
To the best of my knowledge, the only person to have looked at the Irish case is Enda Hargaden, who is now at UCD. He finds that the elasticity of taxable income is 3-4x higher at economic peaks than at troughs. The basic idea is that, when there is a recession, there are fewer margins of behavioural adjustment in response to taxes – and thus, fewer opportunities to create deadweight loss. It’s harder to adjust your hours when your employer is making layoffs. And people are more responsive to the tax system while the going is good; they have more freedom to engage in activities that minimise their tax bill.14 This is potentially a major problem for any effort to understand the distortion of taxation in a volatile open economy.
Translating the gap between the peak and trough of the ETI curve into how different the marginal cost of public funds should be is difficult, because, remember, we’re in a world of convex, not linear, relationships.
We’re caught between a rock and a hard place. To get enough data to have a chance of saying something rigorous about the distortion of tax on the Irish economy, you need a long time period. And the granularity of individual taxpayer data required to credibly estimate these numbers didn’t really exist in Ireland until the early 2000s.
That means that, necessarily, you’re going to be averaging economic variables across a major boom-bust cycle. The methodologies of public finance have come a long way, and the papers I’ve included here are all very impressive pieces of work. In the long run, we’ll probably figure out Ireland’s marginal cost of public funds. But, to quote one of my favourite economists, in the long run, we’re all dead.
To pull from Keynes again, this does not defeat the conventional wisdom that government spending should be lowest during a boom, and ramp up during a recession. Hargaden adds nuance to this by showing that we should expect MCPF to shift noticeably over time in a volatile economy like Ireland’s.
There isn’t really a suggestion in the paper that the elasticity of taxable income is more volatile per unit of economic downturn than in other countries. It’s just that the recession in Ireland was so catastrophic – quadruple the proportionate economic decline compared to America – that it’s a good fit for identifying the true effect.
Modern cost-benefit analysis
So far, this post has been extremely theoretical. I’m somewhat amazed that Seán let me include equations. But does anybody actually care about this? How does the Irish government account for the distortionary effects of taxation?
Treatment of this issue can be found in section five of the technical appendix to the Public Spending Code.15 It recommends that all government departments and agencies apply an MCPF multiplier of 1.3 to cost-benefit analysis.
In my ideal world, the amount of scrutiny a project received would scale as its benefit-to-cost ratio approached the threshold for the marginal cost of public funds. And the perfect cost-benefit analysis would account for where we’re going to get the marginal euro from.
There was a review of this approach in 2018 by the Irish Government Economic and Evaluation Service (IGEES), which concluded that the 1.3 number was still appropriate.16 The current number has been in place since 2015; previously, numbers between 1.25 and 1.5 were used, depending on the department.17
How did they reach this number?
As far as I can tell, there was no specific piece of research that recommended 1.3. Acheson et al. is not the only attempt to find Ireland’s MCPF, although it is by far the most up-to-date and rigorous. The first attempt at it was by Patrick Honohan and Ian Irvine in 1987. They found an eye-watering MCPF of 2.44; see context from John FitzGerald on how they arrived at so large a number.
One of the key intuitions is the rule of thumb that the distortion associated with a tax scales as the square of its value – a callback to the geometry of the Harberger triangle. Double a tax, and you tend to get four times as much deadweight loss. In the 1980s, the modern methods hadn’t been developed yet, so the best economists could do was apply the Harberger triangle, which only really works for small changes in tax.18 Honohan later wrote that after Ireland’s top marginal rates were reduced, MCPF fell to 1.5. The Public Spending Code’s figure of 1.3 was presumably a compromise between the Acheson paper, Honohan’s work, and international evidence. References to the Public Spending Code sometimes say that the 1.3 figure was “derived theoretically”, which strikes me as, uhm, a generous description.
It’s hard to tell from the outside how much these corrections for MCPF actually matter. If you’re being cynical, you might expect that it’s applied selectively: for projects with political will behind them, the distortions of taxation are ignored, but when there is more of an organised resistance, the marginal cost of public funds is used to raise the evidentiary bar for government spending. From speaking with civil servants, the MCPF multiplier seems to be primarily important at the stage of departments presenting the business case for an investment. One civil servant told me about a project that was considered “dead in the water” because its benefit-to-cost ratio didn’t exceed 1.3, which I found to be an encouraging sign.
However, once a project has gotten the green light and commences, you’re really in the realm of politics, not of economics. There’s no database of Irish retrospective cost-benefit analyses, indicating whether their eventual benefits justified the true cost. Frankly, that would be a great subject for another Progress Ireland vibecoded microsite.
The marginal cost of public funds will often be found in the appendix of the reports on major projects, such as those from Transport Infrastructure Ireland. Their cost-benefit ratio for the proposed MetroLink in Dublin is only 1.4, which clears their own bar, but just barely.19
In this respect, Ireland is already doing better than the vast majority of countries. Using an MCPF multiplier is not recommended in the UK’s appraisal guidance (the ‘Green Book’), although some individual departments occasionally still choose to include it.20 The Public Spending Code has a table that compares how it is doing with the comparator countries they studied:
As you can see, Ireland is on the high end internationally. Multipliers above 1.3 are occasionally used in the United States and in Canada, which don’t have a nationwide MCPF figure, but departments and agencies still account for tax distortions in a more decentralised fashion. Ireland’s MCPF value is on the high end, and is unusually explicit.
Some taxes are vastly more distortionary than others
Like many of my projects, I started this post falsely thinking it would be easy to finish. We started with a seemingly simple question about how much deadweight loss is created by tax, but even gesturing toward an answer has required a whirlwind tour through modern public finance.
We started by looking at the elasticity of taxable income, and mathematical derivations for the conditions under which it acts as a sufficient statistic for the welfare loss due to taxation. We then looked at an effort to use this to calculate the marginal cost of public funds for Ireland as a whole. The considerations for whether these methods underestimate the true cost of tax are subtle, but I’m inclined to think they do. We considered the cyclicality of the marginal cost of public funds, and then briefly looked at how Ireland and other countries incorporate these considerations into cost-benefit analysis.
You can see why economists enjoy these thorny intellectual puzzles so much, and it’s easy to get nerdsniped. But none of this should distract us from the much simpler fact that some forms of tax are vastly more distortionary than others. Some taxes create economic effects that are wildly disproportionate to the amount of revenue raised. In the analysis used by the OECD, corporation tax is considered to be the most distortionary major category of tax. Stamp duty is even worse, with many estimates for its marginal cost of public funds being 3+. When stamp duty increases, the rate at which buildings change hands falls dramatically. This is why economists almost universally regard it as a terrible tax.21
On the other hand, property tax is frequently thought to create minimal economic distortion. The theory of land tax is based on the idea that, since land is supplied completely inelastically, taxing it induces no deadweight loss. This was the great insight of Henry George. There are considerations other than efficiency in evaluating taxes, but this is the main reason why I follow Barra Roantree in believing that Ireland’s local property tax is far too low.
That Ireland is reliant on highly distortionary taxes, and raises so little from a tax that is internationally lauded for creating almost no harm to the economy, sounds like bad news to me.
You might well disagree with my assessments of which taxes are good and which are bad. That’s fine. My point is that the distortions due to taxation should be absolutely central to the public discussion about government spending. Instead, they’re virtually absent.
Ireland’s treatment of the marginal cost of public funds is better than most governments, which often brush it under the rug. There is an enormous body of evidence about the indirect effects of all sorts of taxes, and about how they are borne by different groups in the population. Fortunately, we all have free will. The state has a choice over how to raise the marginal euro, and from whom.
Sam Enright is Innovation Policy Lead at Progress Ireland, and editor-in-chief of The Fitzwilliam. You can email him at sam@progressireland.org. He also runs a bounty system to find and catalogue mistakes he has made.
Eoin O’Malley kindly referenced that blog in The Independent.
Deadweight loss was also covered in the corporation tax post.
A very different aspect of Arnold Harberger’s work was the subject of part three of my essay on corporation tax.
The traditional framing of the MCPF is as the face value of a tax plus its deadweight loss. Here is one way that this fails to account for income effects in a particularly embarrassing way. A lump sum tax is a hypothetical tax of an equal amount on every member of the population. This is useful as a thought experiment because, since there is no way to avoid it, a lump sum tax would not change anyone’s behaviour, and thus, has zero deadweight loss. But there will be an income effect from the lump sum tax, because people are poorer, and thus, marginal cost of public funds will be greater than one. This is why some people criticise MCPF for setting too high a bar for government spending. Even if there were no deadweight loss from tax, this framework would still recommend against net-positive investments.
Other economists have argued that, because of this contamination from income effects, MCPF and the actual economic loss from taxation are not even necessarily related. Prominent figures like Stiglitz, Dasgupta, and Stern have argued that the MCPF multiplier is conceptually incoherent.
There are also more technical issues at play, like that the MCPF figure depends on an arbitrary choice of which tax you normalise to zero (the ‘numéraire’ good).
These critics still think that we should account for the distortionary effects of taxation. They just think that that should already been done in accounting for the ‘shadow prices’ of the inputs. For example, if funding the construction of a bridge by raising income tax would reduce working hours, then that should already have been accounted for in a ‘shadow price labour’ which included opportunity cost. Louis Kaplow has shown that, in an optimal tax system that was taking shadow prices into account, the marginal cost of public funds would always be exactly one.
This is an interesting theoretical debate, but I am yet to be convinced it is of much practical relevance. Governments have to choose some framework for cost-benefit analysis, and it’s better to account for distortions than not. I am open to being persuaded otherwise, but it’s not clear to me that we’ve come up with anything better than a marginal cost of public funds multiplier.
These days, you’re starting to hear more about a proposed alternative called marginal value of public funds (MVPF). There’s nothing inherently wrong with a euro of tax causing €1.30 in distortions, provided that there’s a corresponding benefit.
The marginal value of public funds is just the benefit-to-cost ratio, accounting for ‘fiscal externalities’, i.e. any downstream effects on tax revenue and government spending generated by the policies. If the state is considering investing in a bridge project, the marginal value of public funds will include all of the ways in which the state’s eventual tax base will be shrunk or grown by the bridge. That idea is simple enough, but there wasn’t a clean conceptual framework for implementing it until the publication of a paper by Hendren and Sprung-Keyser in 2020, which inspired the Policy Impacts initiative at MIT. The idea is that MVPF could be a single number by which we could compare cost-benefit figures for different projects, without having to apply an MCPF multiplier. However, it is still quite niche and theoretical.
This was a joint project between the Department of Finance, the ESRI, and the Revenue Commissioners.
The appendix of Acheson, Stanley, Kennedy, and Morgenroth contains a table of ETI estimates for different countries.
Another way that the elasticity of taxable income breaks down as a sufficient statistic is when behaviours have externalities. That is a good reason for treating carbon taxes and other taxes on externalities separately from taxing productive economic activity.
Interestingly, a major exception to this rule of thumb is married women, whose working hours respond significantly to higher taxes; see Saez et al., page four.
Note also that the formulas we’re using in this post are about a one-period optimisation problem. Modelling intertemporal issues tractably and identifying them empirically is really tough.
Employee PRSI is 4.2 per cent, while employer PRSI is 11.25 per cent. However, much of the previous post was about explaining why legal incidence does not determine economic incidence. If you subscribe to this idea, both forms of PRSI are economically identical.
ɑ is defined as z_m/(z_m - z*), where z* is the threshold after which income is assumed to be power-law distributed, and z_m is the mean income about that threshold.
Confusingly, in this area, ‘income tax’ refers to the marginal tax on income from any source, which is not the same as what administratively appears under the name ‘income tax’. This, again, is a callback to my previous essay: names of taxes are often misleading compared with the economic concept they correspond (or fail to correspond) to.
Britain’s National Insurance is more-or-less equivalent to PRSI in Ireland.
Another family of approaches to estimating MCPF called computable general equilibrium (CGE). This is a way of writing down the whole economy as a system gotof equations covering production, consumption, government, and trade, and calibrating it to data from a country in a base year. You then simulate a policy change and see what the new equilibrium looks like. In theory, if you take the ratio between the welfare change and the net revenue change, you can read off marginal cost of public funds from these models.
Unlike papers in the tradition of Saez, which are rarely if ever able to account for anything other income tax, CGE includes many other taxes, including environmental taxes, VAT. The only application of these models to Ireland comes from a working paper from researchers at the European Commission, resulting in a value of 1.33 for labour taxes and 0.62 for ‘green taxes’, which, confusingly, they model as just a tax on household energy consumption. For the UK, these values are 1.81 and 1.13, respectively. For the EU as a whole, the average MCPF for labour taxes is 1.9 and green taxes is 1.08.
This looks like remarkable convergence. Two two entirely different methods converged on an MCPF figure for Ireland within 0.02 of one another. But I’m putting this in a footnote because I think this is basically a coincidence: Acheson et al. covers data from 2004 and 2015, while the European Commission paper is a snapshot from 2005. But 2011 was a year of major tax reform for Ireland, including the introduction of universal social charge. Even if the methodology were perfect, we shouldn’t estimates from different time periods to converge upon such similar numbers.
Still, it is of interest, in line with McClements’s post, that tax in Britain is more distortionary than it is in Ireland.
Hargaden finds an overall ETI of 0.06, which is almost three times smaller than the best available estimate. Due to the frictions of actually taking advantage of tax changes and some causal inference issues, the estimates that you get from Hargaden-style bunching analysis are usually interpreted as lower bounds that substantially underestimate the true elasticities.
Beginning in 2024, the Public Spending Code was phased out in favour of the Infrastructure Guidelines. However, it’s being phased in stages, and I can’t find any evidence that the treatment of technical parameters such as MCPF and the social discount rate has changed.
The report has experienced link rot, but has been saved for our purposes by the Internet Archive. I chuckled at this quote page 42, an instance of the general rule that the phrase ‘of course’ is usually followed by your most controversial premise: “Typically, the costs of a project are of course offset on the benefit side of the appraisal by valuations of impacts”.
See page 46 of the report. More generally, the 2018 review by IGEES gives a surprisingly detailed intellectual history.
See Saez et al., page 8.
The cost-benefit analysis was much more favourable when it was evaluated in 2018, giving a benefit-to-cost ratio of between 2.4 and 3.0, but that was before substantial inflation in construction costs. If you ask me, understanding and responding appropriately to out-of-control costs in infrastructure is one of the key issues of our time.
This 1.4 number already bakes in an assumption about future benefits being less important than present ones, through a social discount rate. Economists and philosophers have long debated about whether and how we should discount future benefits in this way, and my undergraduate dissertation was about one specific and ridiculously niche application of this idea. In a future post, I’d like to return to the topic of how the government selects these discount rates, which is hugely consequential but rarely discussed.
That doesn’t mean Britain ignores distortions from taxes entirely. In principle, the cost of public funds is implicitly built into how budgets are allocated across departments.
I am somewhat bemused that the Irish public discussion has tended to treat the raising of stamp duty as a relatively technical revenue-raising matter, in a way that elides how economically contentious it is.
Interesting article on evaluating public spending and opportunity costs.
One area where getting better value from public money really matters is NHS staff pay and retention in the UK. A useful tool for understanding how NHS pay bands, increments, and take-home pay actually work is here: https://nhspaycalculatorss.co.uk/
This kind of transparency could be helpful for Ireland’s public sector pay discussions too.