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

Matt Nolan looks at why we have income taxes, their benefits and the problems with efficiency and 'deadweight losses'
Part four of a six part series on tax.

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 »

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if it is large enough the tax will just stop land being used.
Not sure that this is right, If the tax is just on the land if it is used or not and is owed no matter what. The people are encouraged to use the land to pay the tax.
The opposite happens in the UK where even rates do not apply if the land is not used so the cost of holding land and not using it approaches zero

I would have said the opposite, ie if its to low (or none) there is no incentive to use it to make a return to pay the tax, hence Im all for a land tax.  The only thing would be that if we had a land tax, PAYE tax and other taxes should be reduced to match such that those paying taxes already see a neutral cost, those paying no tax find they pay. 
regards

Overall in your articles to date on the topic I am not sure if you have really covered why modern governments tax at all. Because we need to understand why we are doing it.
If Governments spend monety into existence they have to tax it out again. In the end they have to tax all or most of the money they spent into the economy out so as not to debase completely the value of money. The only people to tax then are the people who have money. There is little point taxing people who have to spend all the money they have simply to live as they do not have much money to pay as tax. So comsumption taxes that are high seem like a stupid idea.
Income tax has its place , land tax definitely has a role to play.
The reason we need to know why we have to tax money out of existence is that it explains why flat tax rates are actually very wrong. It actually explains why progressive taxes work better than regressive ones.

Interestingly in the past there seemed to be no justification for progressive taxes except as a choice of society.  Yet the articles I am seeing now actually point to the fact that progressive taxes even up to 70% for very high income earners are not detrimental, the tax rate that is critical and impacts the economy is the lower and middle tax brackets.  On top of that however there are ppl who with good accountants not only avoid most tax but appear to be so poor they get WFF....
That's just screwed and hence a land tax looks to be a partical solution to that.
PS The poor will pay tax, they have no choice, so what that means is they spend less to meet their tax obligations. So consumption taxes are bad,  they take essentials off ppl and they are regressive ie they benefit the rich who dont need any such help.
regards 

"the articles I am seeing now actually point to the fact that progressive taxes even up to 70% for very high income earners are not detrimental"
We don't have to read articles, we can simply watch how the french go, they are now running very progressive tax systems on income.
 
"the tax rate that is critical and impacts the economy is the lower and middle tax brackets"
Conversely, without that tax the budget cannot be met.
 
"PS The poor will pay tax, they have no choice"
That's slightly obtuse because although there is front end taxation transfer payments back from the government mean a large percentage of New Zealanders (the poor) do not pay any net tax.

I wasnt quoting the NZ tax situation specifically but commenting on progressive tax policies generally.
French, the simple case there is "all else being equal"  or compare apples with apples.  So is the UK less progressive? that looks like its doing well doesnt it.  Ireland with its 14% tax rate on corporates? basket case that one is it not? asking for more time to pay? 
NZ poor, and so Ok they pay no Net tax, (thats WFF you are refering to?) In which case poorly paid childless singles and couples get no such relief.  It also doesnt apply to welfare, though I suspect it shouldnt.  Even in this case because they still dont have disposable or discretionary income they in effect have no choices.
"The budget cannot be met" I agree that there has to be tax, its the bulk of ppl, but from what I can see there seems to be considerable scope to level and broaden the tax system and releave areas paying more than their fair share.
regards
 
 

Matt,
No real arguments. From where we are now, a modest land or property tax would be okay- and I would personally prefer it to a capital gains tax. Unless there is a particular need for more tax to keep inflation in check, then I agree with Plan B that a trade off with other taxes should be made. Strict equity vs other income probably strictly supports the CGT; while property/land taxes may cause problems for asset rich/ cash poor people. Nevertheless land/property taxes would give greater certainty to both parties of what taxes were payable each year, and they would be in bite sized chunks. In a rising property market, it is not hard to see that a CGT could cause different problems, by dropping people down a rung when they sold and bought in a similar market.
Plan B makes some good points re establishing exactly why we tax, (and there are fundamental questions there, tied in with how monetary policy is run) and I'll look forward to the views on those issues you've indicated will come in the fifth instalment.
The one area I somewhat disagree with him on, is that given we have a high current account deficit; high private indebtedness, and trading industries and their owners are struggling, then further encouraging consumption over income may not necessarily give the right message. There may be other ways to support those people who have relatively little income- arguably WFF already does. It's not a stronly held view though, and happy to have the debate.

Roped into the taxxtion debate is the historical baggage that everyone should pay some kind of tax to have a share in the government. No tax equals no vote - or expressed in reverse - No tax without representation. An idea wars have been fought over.
 
Also, perhaps the phase "tax on capital" needs to be unpacked somewhat. There is the concept of productive investment and unproductive investment and the article seems to lump the two together.
 
Is it morally right to charge interest?  Some major philosophies say no and would link that kind of direct return on money with taxation on a moral basis.

The WHY we tax and WHERE it goes etc will always be there.
 
The current taxation system is a 20th Century tool which is completely outdated.
NZ and other Countries need a taxation system which is in the 21st Century.
The current system sees those who have the ability and can manage the business risk on both the positive and negative side as being accountable for the full management, collection and payment of all taxes. Those that have ability are being unfairly penalised for that ability.
 
The costs to business in keeping all the different records and payment of the numerous taxes is horrendous. The business has the added costs of accountants etc on top. Politicians recklessly redistribute and further salt is rubbed into the festering business wound in watching public servants across the country running incompetent ships and generally being very demanding.
 
I have run some very basic figures through and there appears to be significant benefits to closely looking at the APT tax. I was quite surprised at the immediate savings in time. labour and other costs that would accompany such a taxation system. It would of course have to be applied across every transaction, no exemptions anywhere.
 
There is lot more transparency in a APT Tax and the Government would save money as no IRD would be necessary.  No GST, No PAYE, No other taxes just one tax on each transaction. An APT Tax would also capture all foreign investment in NZ.