Progressivity, how does that work?
Thu 8 Aug 2013 by Matt Nolan in Government

As a note, so far in this series on tax the following issues have been touched on: Why do we tax? What are the distortions of tax? What are poll taxes, and how does fairness matter? What are factor/income taxes? What are consumption taxes? Where does inequality fit in?

In our past articles we’ve built up a stock of ideas that help us to think about what different types of taxes are.  Now we can take an additional step and start to talk about the shape of a tax – namely what progressive, regressive, and flat taxes are.  Armed with this and our previous discussions of burden and fairness we can try to articulate what these three terms mean, and the key features we need to think about when trying to recognise who actually faces the tax – and what the distributional consequences of a tax really are.

One of the main reasons I wanted to write this series on taxation is to help disabuse the notion that a tax works by just picking up resources from a selected group and shuffling them off to another group through spending.  When I mentioned the idea of elasticity and burden it was pointed out that the individuals or group that end up “paying” the tax aren’t necessarily the people you directly liable for the tax.

Before getting to this, we should describe exactly what a progressive, flat, and regressive tax is.

Different shapes and sizes

To think about what sort of name to give a tax we need to stand back from describing the tax as being on a “worker” or on an “industry”.  Instead, we need to think in terms of broad markets and transactions.

A progressive tax implies that, as the base value-added of transactions you are involved with rises, the greater the proportion of the value of these transactions you pay in tax. 

This is quite a hairy way of saying it, so let us think in terms of income taxes.  Your gross income is what is taxed – this is the price your employer is paying for your work.

A progressive income tax implies that, as your gross income rises, the tax that is paid on your income rises MORE than proportionally – if your gross income doubles the tax paid more than doubles.

A flat income tax implies that, as your gross income rises, the tax that is paid on your gross income rises at the same rate– if your gross income doubles the tax paid doubles.

A regressive income tax implies that, as your gross income rises, the tax that is paid on your gross income rises at a slower rate– if your gross income doubles the tax paid less than doubles.

The intention of our tax system is to make sure that those with a higher ability to pay do indeed pay more.  This, as we previously mentioned, is vertical equity.  When we talk about principles related to inequality this is what we are often interested in.

Progressive, flat, and many types of regressive taxes all satisfy some version of this principle in terms of the amount of tax paid – the individual who has a higher income is paying more tax on this income.  But the more progressive a system is, the greater the proportion of tax is paid in situations where higher incomes are accrued.

Simple enough – so we just need an assumption about fairness?

Here is where things get complicated.  Remember that wages, and incomes and prices, aren’t set in stone in some mystical “book of income and prices”.  Income paid to an employee is set in a market – where the employee is selling their labour to an employer.  Depending on their relative bargaining position, and their relative responsiveness to the tax, the question of who ends up “paying the tax” (the employer, or the employee) is an open one.

We can even go a step further.  The employer is only hiring the employee based on what they can sell their product for.  When a tax increases the cost of employment, this may in turn lead to the employer having to change the price they pay for the product they sell.  In the end, we have a set of interrelated markets where the burden of taxation is being shared – with higher prices for the goods and services purchased by consumers accounting for part of the burden of taxation!

Now when it comes to our idea of vertical equity, as a society we may have some belief about what is fair – and about the way that redistribution should occur based on the differences in ability between individuals. 

The implied goal of policy makers when they set up a progressive income tax is to redistribute proportionally more goods and services from those with the ability to get them to those who do not.  If we could target ability directly and throw a lump sum tax on it, this would be fine – but since we cannot we must suffer the impact of trying to chase those with high ability through taxes on the transactions they make with other people!

As a result, we need to recognise that the burden of the tax does not necessarily fall on whatever person, or even group, that we may aim to target.

Does this relate back to efficiency at all?

In this sense there is an interesting relationship between the way the tax can impact upon these views of fairness, the burden of taxation, and the impact it has on efficiency.

The more progressive a tax system is, the more the burden of tax will be shifted to the transactions associated with high income earners.  For now, let us put to the side the way more general prices change, and act as if increasing the progressivity of the tax system simply shifts the burden of taxation from low income to high income earners.

Given this, we know that an increase in progressivity implies that the marginal tax rate for high income earners must rise, while for the same level of spending the marginal tax rate for low income earners will be lower.  A marginal tax rate is the tax rate you would pay if you earned an additional dollar from employment.

At a given wage level, this marginal tax rate will have an impact on the incentive to supply labour.   By creating a gap between the social and private value of the work the individual does, it will lead to people working too little by either cutting back hours (the intensive margin), pulling out of the labour force (the extensive margin), or pulling back from building up skills (human capital).  Furthermore, higher marginal tax rates combined with a complicated tax system can lead to types of tax avoidance – such as shifting the timing of income payments, moving income into trusts, or changing the individuals within a family unit that the taxable income accrues to.

To some, this idea may not pass the initial smell test and so they may try to ignore it.  However, the data suggests that this is something that does indeed exist.

About this time last year Treasury released a working paper on “The Elasticity of Taxable Income in New Zealand”.  The paper states “a feature of the results presented here, shared by a number of studies for other countries, is that they indicate quite substantial values (in excess of 0.5) of the elasticity of taxable income for high-income individuals”.

As a result, for high income earners an increase in marginal tax rates leads to taxable income being shifted and/or labour supply incentives changing.  The aforementioned paper points out that, the significant response of high income earners to changes in marginal tax rates implies there are significant marginal welfare costs (leakages, or the loss in income from the increase in the tax rate, relative to the case where no change in behaviour occurs) from increasing the marginal tax rate on high income earners.  These behaviour shifts are something that needs to be taken into consideration as an important constraint when choosing a level of progressivity in the tax system.

Furthermore, these estimates are only for the short term cost – as we noted when we mentioned human capital a tax on higher incomes will also reduce the return from investing in skills and education.  As a result, there is a further long-term cost to efficiency from progressivity – that comes from a drop in the accumulation of capital.  An issue we touched on here.

Some may say that this is excessive – surely reducing the return to education can’t have that much of an impact.  This is an empirical point where a lot of research is taking place and is an open question, and so it is a fair one.  However, if we believe the progressivity of the tax system (and lower returns to education) does not have much of an impact on capital accumulation we MUST also believe that increasing the returns to education will not have much of an impact through other policy channels – too many people are inconsistent with their beliefs between these two!

Where does this leave us?

In today’s article we discussed progressivity, and the complicated interrelationships between ideas of equity and efficiency.  Given these difficulties, it is important for policy makers and researchers to clearly communicate the trade-off that exist – so that an informed public can come to some conclusion about what they think is fair.

While the principles of tax we recently mentioned helped us to understand some of the interrelationships, the importance of elasticity in determining who actually pays a tax was made apparent here – just saying “I want that person to pay” doesn’t work when they can pass the buck on or shift away from paying tax altogether! 

Furthermore, even if higher tax rates are able to redistribute income (in terms of the goods and services available to different income groups) the impact on people’s willingness to supply labour and the wedge between the private and social benefits of someone’s decision to work does imply there are efficiency costs from doing so.

Now do not let people use this as an excuse to ignore issues of fairness and redistribution, the fact that issues are complicated does not mean we should all stop asking what we believe is right for society and the communities we live in.  However, hopefully it helps to explain why many economists hint at a flat tax system with a bunch of progressive transfers on the spending side – as this seems like a way to achieve any fairness goals that is clearer and more transparent.

Contrary to common belief, economists are not trying to stop society agreeing on principles of fairness by raising these issues – we just want the conversation to be had in a clear way.

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