Matt Nolan looks at why we have income taxes, their benefits and the problems with efficiency and 'deadweight losses'

By Matthew Nolan*

This is the fourth article in a series on taxation.  The previous articles in this series can be found in the following places:  Why do we tax, tax distortions and burden, the non-ideal ideal tax.

As was pointed out in the previous article on tax, as a society we care about more than just strict efficiency when we set up the tax system.

We also want to ensure that those with the ability to pay more do indeed pay more. 

Since we cannot observe an individual’s ability, in an “efficient” system we may struggle to redistribute to the worst off in society – and as a result we have a clear “equity-efficiency” trade-off.

It is with this principle in mind that we moved towards the tax system we have today, with a mix of income and consumption taxes the dominant part of government revenue.  We will discuss these, and the trade-offs associated with such taxes, in the next three articles.

Today we will outline the idea of income tax.

Ability and factors of production

Previously we had discussed how, if we could place a lump-sum tax on individual’s based on their “ability” we could use this tax as a way to pay for government produced goods and services for the public at large. 

Such a tax would be both efficient (in terms of not involving a “deadweight loss” – the loss in the value of output due to a wedge between the price paid and the price received for a good or service) and “fair” in so far we care about the idea of vertical equity (those with a higher ability to earn should pay more tax) and horizontal equity (those with the same ability to earn should pay the same tax).

However, we cannot observe ability, and discriminatory lump-sum taxes on factors related to ability (eg height, sex, race etc) are also seen as socially unacceptable.

Given this, society has moved towards a different type of “ability” tax – a tax on income, or more generally the factors of production.

The fruit of someone’s ability comes from the income they earn. Individuals earn labour income when they sell their labour, capital income when they utilise their capital, and gain income on land when they use their land.

The ability to earn income from these factors of production that a person has on hand is very much the type of ability we have in mind when considering forms of equity and fairness.

However, there is a huge difference between taxing someone’s ability to earn income from these factors and taxing the income that is earned from these factors ! This comes back to our aforementioned idea of efficiency, and the deadweight loss of taxation that we mentioned in article two.

Returning to elasticities

In order to understand the difference between taxing the ability to earn and taxing earnings, we need to go back to article two and brush up on the idea of elasticity.

According to a simplified version of this concept, the more that the quantity supplied and demanded for a good or service changes when the price changes, the greater the inefficiency (dead-weight loss) is.

As a result, the more responsive supply and demand for a good (in this case a factor of production) are the less efficient the tax will be when it creates a “wedge” between the price received by the seller and the price paid by the person buying it.  Namely for a certain level of government revenue, the value to buyers and sellers of transactions that do not take place due to the tax will be higher the more elastic supply and demand are.

For example, in the labour market the gap between the price paid and price received due to tax is the difference between the gross wage and the net wage.

Now there are firms who would hire people for more than the net wage, but less than the gross wage.  And there are people who would work for less than the gross wage, but more than the net wage.

As a result, the employment that gets priced out of the market by this wedge, and the value associated with it, is the dead weight loss.

If we tax the inherent ability to earn income, we do not change this “price”. But if we tax income itself, we do create this wedge. That is the inefficiency.

Relative inefficiencies

However, when we previously discussed inefficiency based on the idea of deadweight loss, we didn’t mention that as the tax increases, the additional deadweight loss also rises.

Essentially, each additional unit of a good or service that is not produced and consumed due to the tax will have had a higher value (in terms of what the purchaser would have paid relative to the price the seller would accept).

As a result, we will want to tax factors that are relatively “more elastic” at a relatively lower rate.

Immediately this suggests to us that a tax on the stock of land is a relatively efficient tax. A lump sum tax on land is unlikely to have much of an impact on the way land is utilised.

This is because the supply of land is fixed, so for a small enough tax this will just lead to land prices dropping and no change the incentives regarding the use of land – and as a result is relatively efficient.

Land taxes are pretty popular among economists. In New Zealand, Andrew Coleman and Arthur Grimes have put a lot of thought into the broad impacts of such a tax.

But, a tax on land is not going to cover off all our needs.

Just like our with previous discussion of poll taxes, we have to accept that the burden of a land tax will fall on specific groups (in this case land owners) and that given our views on vertical and horizontal equity this burden may be seen as unfair. Furthermore, if it is large enough the tax will just stop land being used.  As a result, we also need to investigate the properties of other factor taxes.

The two taxes we will think about here are labour income taxes and capital income taxes. Both of which are subject to the “wedge” issue we discussed above. As a result, for a first approximation of which type of tax we should focus on we will want to look at relative elasticities.

However, there is an additional issue that must be looked into in order to pick the “right” elasticities – time.

Adding a time dimension

We often hear people say that taxes on labour income are preferable to taxes on capital income. If we were looking at things at a “point in time”, we would state that this seems a bit rough.

When we are talking about a point in time, we are discussing “static” concepts.  For example, we may believe there a fixed stock of capital at a point in time, but workers could easily supply more or less labour (thereby spending less or more time enjoying leisure), potentially implying that a tax on labour may be more responsive.

But there is a reason economists have this view.  Time.

This result was formalised, by Judd and Chamley with the two authors showing the same result at the same time (although they worked on it separately). 

The taxation of capital income raises revenue right now by taxing the return on existing capital. However, as this capital depreciates and needs to be replaced, and as people think about investing in new capital, this tax reduces the incentive to invest. As a result, the taxation of capital income reduces the incentive for people to accumulate capital.

What this means is that the inefficiency over the longer term is a lot larger than the loss of efficiency we may expect if we only think about this in a static sense. This is the dynamic (over time) impact of capital taxation.

Essentially, if we think about capital tax in a dynamic sense, the supply of capital used for production is a lot more responsive to taxation (it is more elastic).  In fact, as a small open economy, capital is a lot more responsive relative to labour when the price changes – and as a result, the inefficiency associated with a tax on capital income is higher than that associated with a labour income tax for raising a fixed amount of revenue (see Chen and Mintz for New Zealand).

This logic has been taken a step further and used to justify a zero rate of tax on capital income as relatively efficient. This is not a hard and fast result, and can break down for a variety of reasons (Piketty and Saez, slides) such as credit constraints, differences in tastes around bequests or the discount rate, and the existence of “non-physical” forms of capital. 

However, the principle of taxation on “capital accumulation” being something that, for efficiency reasons, we should tax much less than other things still – not just for physical capital but for human capital as well.

As a result, the increasing importance of human capital accumulation (building up skills, knowledge, experience with certain elements of your job) implies that the even just the shape of the efficiency trade-off between capital and income taxes is very complicated and has been changing through time.

Conclusion

Here it was established that, although a land tax has some nice properties, a tax on income may also be necessary to finance government spending.

As a result, to determine how to split the burden of income taxes between different types of income (on efficiency grounds) we need to ask how responsive the quantity supplied and demanded will be to the introduction of the tax.

However, it turns out we can make more sense of this debate by looking at consumption taxes.

Next time around we will touch on why consumption taxes have many similarities to income taxes – and as a result we will introduce another welfare principle that people may care about.

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Matt Nolan is a senior economist at Infometrics. You can contact him here »