Tax Incidence

Every Chancellor likes to pull a rabbit out of their hat during the budget, and this Chancellor is no different.  Like any good showman, he left his rabbit until the very end.  He announced he would be abolishing stamp duty on all properties purchased by first time buyers below £300,000.  This was announced as a measure to help first time buyers.  It took most economists worth their salt about 10 seconds to realise that this measure would not help first time buyers, but would simply lead to higher prices, and real effect was a transfer of resources from the tax payer to home owners.  Of course, the OBR (who are economists and worth their salt) had already pointed this out in their blue book accompanying the budget.

Most economists would be quick off the mark here because it is one of the first lessons taught in Econ101 that the formal incidence of a tax and the effective incidence of a tax are completely independent.  The formal incidence of a tax is a question of who is legally responsible for paying a tax.  The effective incidence of a tax is asking who actually ends up paying for the tax after all is said and done.  Governments can change the formal incidence of a tax as much as they like, but it will have no impact on the effective incidence of a tax. 

This is something that can demonstrated through one of the most common economic models, supply and demand.  Let's start by thinking of the market for widgets.  Suppose that the demand curve for widgets is described by the following equation: p = 100-q.  Suppose that the supply curve is described by p= 3q.  The price moves until the number of units consumers want to consume is the same as the number of units suppliers are willing to supply, which will be where the demand and supply curves meet.  This is where 3q = 100-q, or 4q = 100, or q=25, which implies a price of p=75.

Now suppose that the government imposes a tax on the sale of widgets in the amount of £10 per widget.  At first we will suppose that buyers are responsible for declaring their widget purchases and paying the tax.  Provided we are careful about our terms, we can work out what will be the effect of this on the market for widgets.  To be consistent, we will always ensure that p represents the amount of money handed over to the supplier by the purchaser.  So consumers now take into account that for every unit they purchase, they will have to hand over £10 to the government.  This will shift the demand curve down by exactly £10, so it becomes p+10 = 100-q => p = 90-q.  think about it like this: whatever the price consumers hand over to the seller, p, they know they know they must hand over an additional 10 to the government, so wherever p used to appear in their demand curve, we replace it with p+10.  So now let's find the equilibrium again, and this will be where 90-q = 3q, which is where 4q=90, which is where q=22.5, so the price handed over to the supplier is p=67.5. Note that this is what the supplier receives for each unit, while the buyer pays 10 more than this, so the price paid by the buyer is p+10=77.5.  So for buyers, the price has only gone up by £2.50, while for sellers it has gone down by £7.50.  Despite formally being responsible for the whole tax, buyers effectively only pay 25% of it, while the sellers pay 75%.

What would happen if the formal responsibility for paying the tax were reversed, and sellers had to report transactions and pay the tax?  In that case, demand would return to its pre-tax relationship, p=100-q, but sellers would take account of their responsibility to hand over £10 for every transaction.  So whatever the price paid, p, they would be aware that they would only receive p-10, and they would respond accordingly.  So their supply curve becomes p-10=3q=> p = 10+3q.  Once again, we can find the equilibrium in the market after the tax is imposed by finding the intersection of demand and supply: 100-q=10+3q => 4q=90 => q=22.5.  Substituting this quantity into the demand curve or the post tax supply curve, we see that the transaction price must be p=77.5.  This is the whole price paid by the consumers for each unit, but the suppliers have to hand over £10 out of this figure to the government.  So the net price received by the suppliers for each unit will be £67.50.  So comparing to the no-tax benchmark, the price paid by the consumers went up by £2.50, while the price received by the suppliers went down by £7.50.  The consumers pay 25% of the tax and the suppliers pay 75%.  The effective division of the tax is exactly the same when the sellers are formally responsible for paying as it is when the buyers are formally responsible for paying. This is what economists mean when they say that the effective incidence of a tax is independent of the formal incidence of a tax.

But we can go further than that.  Why did most of the tax burden fall on the suppliers?  To get the intuition here it is useful to look at supply and demand on a diagram.  In the diagram below we have graphed supply and demand.  The grey line shows the pre-tax equilibrium.  The dashed black lines show the post tax price paid by the consumer and price received by the supplier. 

The impact of the tax is that the new equilibrium must be where the price paid by the consumer is £10 more than the price received by the supplier.  Effectively it drives a wedge between supply and demand.  Because the supply curve is steeper than the demand curve, this wedge involves a larger price fall for the supplier than price rise for the purchaser.  This is actually a general result.  The more inelastic side (i.e. the side with the steeper curve) of the market will pay more of the tax.  How much more of the tax they pay is in proportion to how much steeper their curve is.

In the UK housing "market", the supply curve is incredibly steep.  It is almost vertical.  This is the key problem in this "market" and why prices have risen so high.  So although buyers are formally responsible for paying stamp duty, the effective incidence is such that virtually all of it is actually paid by the seller in the form of lower prices.  If you cut stamp duty, sellers don't have to pay so much of the tax, and the means through which this happens is higher prices.

So whenever the chancellor announces a tax cut remember that the benefits don't necessarily accrue to the party officially paying the tax.  They will accrue to the people who are actually paying the tax, and they won't always be obvious.  One needs to think about what is being taxed and whether the buyers or the sellers are on the more inelastic side of that market.

Hostile Odds

According to The Guardian, the government, in its attempt to create a “hostile environment” for illegal immigrants, has recruited the banks into doing immigration checks on 70m current accounts.  That is just slightly more than the population of the UK, and not everyone in the UK actually has a Current Account.  I can only assume this means the government is asking the banks to check the immigration status of literally every current account holder in the UK!

In the process, according to the Guardian story, the “Home Office expects to identify 6,000 visa overstayers, failed asylum seekers, and foreign national offenders.”  The guardian story also informs us that “The accounts of those identified will be closed down or frozen.”

The Guardian story continues “Banks have been told to adopt a default position of telling customers to take up the matter with the Home Office if a mistake has been made, even if they provide a passport or biometric residence permit showing they are lawfully present in Britain…

“The new legislation requires the banks to check the identity of every current account holder against a Home Office supplied database held by an anti-fraud organisation, Cifas.”  So it looks like this is going to be an exercise in matching names of current account holders to a list of potential immigration rule violators.  So if someone who is here illegally has opened the bank account with a slightly different spelling of their name, they will be missed and there will be a false negative.  If someone with a perfectly legal right to be here just happens to have the same name as someone who is on this list, there will be a false positive.  That person will find their account frozen and will have to deal with the Home Office in order to unfreeze it – an experience which by all accounts compares favourably with banging one’s head against a wall.

Let’s run the numbers and assume that the Home Office are correct in their estimate that there are 6,000 people here illegally who also have current accounts. Given their recent performance overestimating the number of foreign students who overstay their visa by over 2,000%, that is stretching credulity.  But let’s go with that for the sake of making some estimates and crunching some numbers. 

Let’s consider some scenarios around the success rate.  Some estimates have suggested the Home Office’s error rate could be as high as 10% (see below).   

So we’ll use that as a worst case scenario.  We’ll run the numbers assuming the Home Office accuracy rate is:

• 90%;
• 99%;
• 99.9%; and
• 99.99%.

Then we can calculate the number of false positives we would expect given this level of accuracy, given that there are 69,994,000 current accounts held by people with every right to be in the UK.  The numbers are in the table below:

Accuracy	90%	99%	99.90%	99.99%
Error Rate	10.00%	1.00%	0.10%	0.01%
No. Of False Positives	6,999,400	699,940	69,994	6,999

In order to cut the number of false positives to be of the same order of magnitude as the number of people they are hoping to catch, the Home Office would need to be 99.99% accurate.  Even then, there are about 1,000 more false positives than the number of overstayers the Home Office expects to catch.  So it would be more likely that someone whose bank account was frozen as a result of this review had a right to be in the UK than not.  Remember this is the same Home Office that was once declared “unfit for purpose” by the minister in charge of it (who was quoting a senior civil servant).  The same Home Office that violated a court order in deporting someone to Afghanistan and may well have been in contempt of court.   The same Home Office that “accidentally” sent letters to over a hundred European citizens exercising their treaty rights living in the UK legally telling them they should pack their bags or face arrest.  To suggest that this Home Office can hit that target level of accuracy is patently absurd.

The next step is to make some assumptions about how quickly civil servants can clear up the confusion that results from false positives and set them right.  We will assume a somewhat optimistic 5 person hours per false positive to clear it all up.  Given some of the stories linked to above, this may be absurdly optimistic.  Remember that is just the time of the civil servants at the Home Office, it is not taking into account the time and effort of the people caught up in this dragnet, neither is it taking into account the time of bank staff.  We will further assume 500 civil servants are dedicated to this task and the cost of civil servant time to the tax payer is £24 per hour as this is the figure used to turn down Freedom of Information requests on the grounds they would cost too much.  On the assumption that these people work 8 hour days and 260 days per year, we can work out how many days and years it would take to clear all the false positives as well.  Those calculations are in the next table:

Accuracy	90%	99%	99.90%	99.99%
Person Hours to clear false positives	34,997,000	3,499,700	349,970	34,997
Hours to clear	69,994	6,999	700	70
Days to clear	8,749	875	87	9
Years to clear	34	3	0	0
Cost	£839,928,000	£83,992,800	£8,399,280	£839,928

Even on the optimistic assumption that the Home Office cuts the proportion of false positives to 10% of what it has been in the past, it would still take around 3 years to process all of the false positives coming out of this exercise.  That is a very long time for some people to be spending in limbo, with no access to their bank accounts, unable to pay the rent, mortgage, unable to pay the gas bill, unable to pay for groceries.  All to try and catch a measly 6,000 or so visa over stayers.

The Home Office might be able to catch a few more illegal immigrants if they expand their search parameters and look for common mis-spellings of the names that are on their list or other variations.  This would reduce the number of false negatives, but it would increase the number of false positives, leaving more innocent people with no means of paying the rent or mortgage or gas bill.

Yes, I’ve had to make a lot of assumptions in making these calculations.  However, at every point, the assumptions I've made are fairly reasonable.  The Home Office could cut the time it takes to clear the number of false positives by dedicating more civil servants to the task.  However this would not cut the total number of hours taken and would not cut the cost of dealing with the backlog, which could run as high as £840m.  Neither would it do much to cut the costs, panic and trauma imposed on thousands, maybe millions of perfectly innocent people.

The numbers work out this way, with so many more false positives than actual illegal immigrants caught because the number of illegal immigrants is just so small (even by the Home Office’s wildly inflated estimates) relative to the size of the UK population as a whole.  Yet the political hysteria surrounding this issue has reached fevered proportions.  The words of Sir Humphrey have never been so apt: “If you’re going to do this damned silly thing, don’t do it in this damned silly way.”

Indeed, these numbers and costs are so dire, that it is amazing to think that anyone could have thought this is a good idea.  Yet this is happening as a result of an Act of Parliament that was passed with full parliamentary scrutiny in both Houses.  Just imagine what these ministers and civil servants would get up to if a law were passed giving them the authority to make their own laws with the full force of an Act of Parliament with no Parliamentary scrutiny whatsoever!