Why the Permanent TSB/ESRI index is likely to be a load of old sh*te. Plus a little refresher in secondary level statistical analysis.

In the next two weeks, the State’s only index on actual sales prices that analyses results by the mix of property sold, will be published in respect of the three months July, August and September 2010. This entry is going to examine the reliability of the Permanent TSB/ESRI (PTSB) house price series and in particular whether the data analysed to produce the results is so small as to give rise to margins of error that are so big as to render the results practically meaningless. The upshot is that in the context of mortgage transactions, the PTSB index probably has a 7-8% margin of error, in other words take their prices and the true price level of all mortgage transactions should be within a range of 8% below PTSB’s prices and 8% above. There is no objective information on cash transactions but the entry below concludes it likely that they would distort prices to lower levels if they were included.

Firstly, let me take most of you back to secondary school. My recollection is that the maths books were pretty dreadful (why or why don’t our schools just have a mass burning of these books and get the books they use in Singapore schools and which savvy parents throughout the world are buying for their progeny). Let’s remind ourselves of some basic terms when trying to make sense of statistics – remember though that the overall aim of the PTSB index is to quantify movements in the price of property from one period to the next based on all transactions.

Population: in the context of analysing prices achieved in property transactions, the population will be the total of all transactions during a period, those subject to stamp duty and those exempt, those mortgage-backed transactions as well as cash sales. Sadly there is no information published on the overall number of transactions in Ireland. The Revenue has that information and may start publishing it next year, I understand. As you can see from the preceding entry on here, the Revenue has made available for the past few years details of transactions on which stamp duty has been paid – unfortunately we don’t know the number of transactions not subject to stamp duty but they will include some first time buyer transactions and sales of new property below 125m2 in area. Another partial source of information is the Irish Banking Federation (IBF) which publishes mortgage drawdown information. The IBF accounts for 95%+ of all mortgage lending in the State but we don’t know how many transactions are not subject to mortgages – “cash sales”. We do know that overall there are some 790,000 extant mortgages in the State and that there are about 1.5m households and about 2m homes. But that doesn’t give us a steer on how many transactions today are effected without a mortgage. So we can use the IBF figures but need to acknowledge that they are a subset of total mortgage-based transactions (95%+) which in turn are a subset of the total population of property transactions. Cash transactions may have different characteristics – on the face of it you would imagine that a cash buyer that is able to conclude a transaction without mortgage-related delays, or indeed the need to obtain mortgage approval in a market that is reputedly starved of credit, might achieve a better price – put that to one side for the moment. So according to the IBF, there were 14,781 transactions in the first six months of 2010 (of which 9,171 related to property transactions whilst the remaining 5,610 were for top-ups or re-mortgages). The value of transactions for the first half was €2.525bn (of which €1.942bn related to property transactions and €0.583bn to the remainder).

Sample type: Samples are supposed to be random and not skewed. That’s not what PTSB mortgage transactions are. You could argue that there are similarities between PTSB mortgages and other mortgages provided in the State, equally you could argue there are differences. You could certainly argue there are differences between mortgage and cash transactions.

Sample size: in the context of the PTSB’s index, this will be the number of transactions in which this company is involved through the issuance of mortgages. I contacted PTSB and asked them to confirm the number of transactions analysed in producing their series but they declined the request citing commercial confidentiality. However their interim report for the first six months of 2010 does provide some information. It states on page 16 that the company issued new mortgages totalling €0.1bn. This may be a rounded number, and if so could represent €50-150m of new lending. But it’s the best we have. If we assume it’s €100m exactly then that represents 3.96% of total new lending by IBF members in the first half of 2010 (and remember that the IBF includes 95%+ of all lending). If we assume the profile of PTSB’s lending is the same as the IBF then that would indicate that the company issued 373 [(PTSB total lending / IBF total lending * property transaction related lending)/average transaction mortgage loan] mortgages during the six month period.

Margin of error (also called confidence interval): This is an indication of how far out your figures might be for any particular confidence level (see below). It should be calculated by reference to the size of your sample relative to the population size. It should also take account of profile differences between your sample and the population as a whole (are PTSB mortgage transactions different to other mortgage company transactions and are mortgage transactions different to cash transactions). You may have seen margins of error expressed in political opinion polls  – say for example you see that Fianna Fail poll 25% +/- 3%, what that means is that you can say with normally a 95% confidence interval (see below) that FF would poll between 22-28%. So what do you think the PTSB margin of error is? If you assume a 95% confidence interval (usual for polls) and in relation to IBF mortgage transactions, 9,171 total for H1, 2010, where PTSB accounts for 373 in H1, 2010 and then divide both by 2 to give you quarterly totals of 4,585 and 186, then you get a 7-8% margin of error (I’m afraid you’ll need trust me, use a free online margin of error/sample size calculator or dig out those old books). That means that the average price of a property in the State in Q2, 2010 was €201, 364 +/- 8% (PTSB Q2) which would give the spread of €185,255 – 217,473 which would equate to 31-41% off peak. Sadly there is no real way of objectively judging whether or not cash transactions are materially different to mortgage transactions – I suggest that commonsense in the present market would suggest that there is a big difference.

Confidence interval: Simply put, the bigger the sample size you more confident you can be in the results. Most polls that you will see have a 95% confidence interval.

Hedonic: Let me gently introduce you to a term which I certainly don’t recall from secondary level (or indeed beyond) – “hedonic”. You might think it had something to do with hedonism but sadly it’s a fairly dry technical concept which simplistically means that when analysing property prices you group together similar transactions (eg all studio flat sales in Ballymun) and then when you compare prices from one period to another, you are comparing apples with apples. And once you compare apples with apples and oranges with oranges, you then figure out how important apples are in the basket you are examining eg say prices on studio flats in Ballymun had increased by 10% from one period to another. And say that  transactions of studio flats in Ballymun represented 5% of all transactions in Dublin, then you would  consider 5% of the increase when compiling your statistics. Hedonic is sometimes referred to as “mix adjusted”. Unbelievably the other source of actual house price information in the State, the DoEHLG (which again looks at mortgage-based transactions only) doesn’t even bother to undertake this basic piece of statistical analyses. The DoEHLG try to bathe their figures in legitimacy by comparing them with the DAFT.ie, myhome.ie (both based on asking prices) and PTSB statistics.

So it would seem that on the face of it when PTSB tell you that price of an average home in the State is €201,364 then  they really mean that they have 95% confidence that it is between €185,255 – 217,473 amongst mortgage-based transactions. Is that reliable? I would have said not because of my feelings towards cash sales. But hasn’t it always been thus? No, PTSB used to have a 20% share of the mortgage market compared to less than 5% today apparently. Also, when the property market was healthy in the sense that there were few distressed sales, when the economy was thriving, when credit was plentiful and where anecdotally, actual prices were close to  asking prices, then cash sales mightn’t have led to lower prices. So no, PTSB market share seems to have dropped and arguably the effect on prices of cash transaction today is markedly different than during the boom years. And what about comparing PTSB with indices produced by other mortgage companies in other countries – don’t they all suffer from the same problems? Well consider the UK where there are two mortgage company house price series, the Nationwide Building Society’s and the Halifax’s. The UK is a far bigger market of course (with 15 x population), the Nationwide and Halifax have about 20% each of the total market (40% total), the UK is anecdotally not suffering from the same credit drought as the State and there is less distress in the property market in the sense that unemployment is lower and the economy has not contracted to same degree as ours. So you might try to argue that PTSB is no different to say the Nationwide, but in reality the Nationwide has a far bigger pool of transactions, 4x the market share in a far bigger mortgage market and a market which hasn’t suffered the same degree of distress as our own.

Of course, PTSB could debunk what I claim above. They could reveal the number of transactions examined (their accounts tell us the total amount of new lending so I don’t see the great commercial confidentiality in knowing on an aggregated basis how many transactions they have examined). They could also reveal the population and I would be particularly interested in this because as far as I can see, the only people to have this are the Revenue and possibly the Land Registry and neither are making the figures public. They might merely tell us their confidence interval and overall margin of error. They might usefully tell us the standard deviation of the different dwelling-type groupings. None of this would require the disclosure of individual transactions and in overall terms is unlikely to tell us anything that the total new lending figure in their accounts don’t already tell us. Because it seems that PTSB is significantly at odds with what estate agents say (and as one commentor said when did we ever believe estate agents but there seems to be a striking similarity in what they are saying and when they’re also claiming we haven’t reached the bottom I can’t see self-interest because potential buyers will be deterred from entering the market until we are at the bottom presumably),  is it not misleading for PTSB not to put a big health warning on their house price series when they reveal the numbers next week?