Strategic Irish Mortgage Arrears: The Smoking Gun

My colleague Tom Flavin and I are preparing a paper for the Dublin Economic Workshop on the financial characteristics of Irish Mortgage defaults. The analysis relies on a donation of anonymized data on mortgage arrears from Permanent TSB and we are grateful to them for their assistance. Tom will give a fuller account of our data analysis at the conference; this blog entry highlights some of the strong evidence for a very substantial proportion of strategic arrears in Irish mortgage arrears.

In US-based research (e.g., Guiso, Sapienza and Zingales, 2011) strategic arrears behaviour has been shown to be significantly affected by the current loan-to-value ratio of a mortgage. Current loan-to-value has no effect on a household’s ability to pay the mortgage, but it has a big potential impact on willingness to pay the mortgage. Current loan-to-value has no short-term cash flow implications (unless the householder is currently selling the property) but it tells the mortgage holder his/her paper gain or loss on the leveraged property investment.

For strategic mortgage delinquents, mortgage payments on a property deep in negative equity (high loan-to-value) is “wasted money” over the medium term since the capital loss is too big to be reversed by random price changes. Strategic arrears are very sensitive to current loan-to-value whereas distressed arrears (legitimate can’t-pays) are completely insensitive to current loan-to-value.

Table 1 shows mortgage defaults sorted by columns into high (greater than 1.4) and low (less than 1.1) current loan-to-value. The data covers all PTSB mortgages in default which have submitted a Standard Financial Statement. Although all principal private residence mortgages in default are required to submit this statement, many ignore this requirement, so the sample is censored. A default is defined as greater than 90 days of accumulated arrears. The sample is sorted by rows into unstressed affordability (ratio of required mortgage payment to net after-tax income less than 20%), stressed affordability (payment to net income ratio less than 30%) and nonaffordability (payment to net income ratio greater than 40%).  The proportion of mortgage defaults falling into the affordable and nonaffordable categories is strongly dependent upon the current loan-to-value ratio. Only 4.6% of defaulted mortgages with low loan-to-value have an affordability ratio in the unstressed affordability category. These are likely to be households where the affordability ratio is mismeasuring some feature of their financial circumstances. The proportion more than doubles (11%) for defaulted mortgages with high current loan-to-value ratios (negative equity mortgages). The same pattern is evident across all the categories.

Table 1: Affordability Categories of Loans in Default

Mortgage Payment to Net Income

Low Loan-to-Value

High Loan-to-Value













Figure 1 shows nonparametric, kernel-based estimates of the proportion of mortgages in default among all mortgages with a Standard Financial Statement, as a function of current loan-to-value. In the absence of strategic default, this graph should be flat. It is in fact sharply upward sloping, particularly above current loan-to-value of 1 (that is, mortgages with negative equity). Note that the sample consists only of mortgages which have submitted an SFS, so it is not all mortgages. That is why the proportion of defaulted mortgages (within this restricted set of mortgages) is so high.

figure 1

Table 2 shows logit and probit models of the probability of default based on loan characteristics. The logit model has technical statistical advantages, but the probit model is preferable here since it is more easily interpreted (the empirical findings are virtually identical for the two models). The evidence indicates that one of the strongest predictors of Irish mortgage default is current loan-to-value, as in US research on strategic mortgage defaults. Consider a mortgage which is perturbed from an affordability ratio of 0.2 to 0.4 (from unstressed to unaffordable). The probability of default for such a mortgage increases by approximately (.386)x(.4-.2)x(.542)=4.18%. Consider a mortgage which is perturbed from a current loan-to-value ratio of 1.5 to 2.0 (such as from a 30% fall in property value). The probability of default for such a mortgage increases by approximately (.386)x(2.0-1.5)x(.3983)=7.69%. The value .386 is from the normal distribution assuming 40% of the mortgages in this sample are in default. More details at the DEW conference on October 18th – 19th in beautiful downtown Limerick.

Table 2: Logit and Probit Estimates of the Probability of Mortgage Default Based on Loan Characteristics

DDV(dist=logit) default

# ppr nonppr nets ltv appnets

Binary Logit – Estimation by Newton-Raphson

Convergence in 4 Iterations. Final criterion was  0.0000000 <=  0.0000100

Dependent Variable DEFAULT

Usable Observations                     31422

Degrees of Freedom                      31417

Skipped/Missing (from 37124)             5702

Log Likelihood                    -20515.8092

Average Likelihood                  0.5205277

Pseudo-R^2                          0.0626346

Log Likelihood(Base)              -21508.3958

LR Test of Coefficients(4)          1985.1731

Significance Level of LR            0.0000000

Variable Coeff Std Error T-Stat Signif


1.  PPR                  -1.298293660  0.046655174    -27.82743  0.00000000

2.  NONPPR               -1.485035539  0.045404048    -32.70712  0.00000000

3.  NETS                  0.883894644  0.032694867     27.03466  0.00000000

4.  LTV                   0.645248662  0.023445407     27.52132  0.00000000

5.  APPNETS              -0.345663177  0.102147798     -3.38395  0.00071451

DDV(dist=probit) default

# ppr nonppr nets ltv appnets

Binary Probit – Estimation by Newton-Raphson

Convergence in  4 Iterations. Final criterion was  0.0000000 <=  0.0000100

Dependent Variable DEFAULT

Usable Observations                     31422

Degrees of Freedom                      31417

Skipped/Missing (from 37124)             5702

Log Likelihood                    -20516.2121

Average Likelihood                  0.5205210

Pseudo-R^2                          0.0626094

Log Likelihood(Base)              -21508.3958

LR Test of Coefficients(4)          1984.3673

Significance Level of LR            0.0000000

Variable Coeff Std Error T-Stat Signif


1.  PPR                 -0.802575009  0.028265540    -28.39412  0.00000000

2.  NONPPR              -0.919901178  0.027459850    -33.49986  0.00000000

3.  NETS                 0.542310980  0.019652259     27.59535  0.00000000

4.  LTV                  0.398303919  0.014320162     27.81420  0.00000000

5.  APPNETS             -0.206773145  0.061545719     -3.35967  0.00078036

Notes: Default = 0/1 default dummy, PPR = 0/1 dummy for principal private residence mortgage, NONPPR = 0/1 dummy for not principal private residence mortgage, NETS = current affordability ratio, LTV = current loan-to-value, APPNETS = affordability ratio at time of mortgage application.



138 thoughts on “Strategic Irish Mortgage Arrears: The Smoking Gun”

  1. Gregory,

    You continually have the cart before the horse.

    If banks were doing their job there would be a lot less vanilla default – and very little “strategic” default.

    You don’t get 12% in arrears of 90-days or more through “strategic” default.

    It seems you want the banks to be absolved of not doing their job and want to make the arrears discussion all about “strategic” default.

    Banks haven’t done their job because it suited them.

    The game is extend-and-pretend.

    The slow resolution of the Dunne judgement, legal letters as long-term solutions, no repossessions… these are strategic decisions by the faintly dim, former rugby players.

    If there is widespread default happening, it’s within the walls of the zombie banks!

  2. Also this tells us NOTHING about ‘strategic’ default. We dont know what that is, but it is generally about “could pay but wont”. Do you have data on net after tax income, other expenses by category etc? If so you might be able to give some light.

  3. As an addendum to the above – if people are “strategically” choosing to not pay their mortgages on underwater/high-LTV properties, it’s because the banks have made it clear that there are no repercussions for this.

    No one is being repossessed. No one is being bankrupted.

    Either mortgages are recourse or they’re not.

    If they are no longer recourse, then banks need to reprice their interest rates to reflect this new reality.

    People have always gone into arrears – it was up to the bank to have systems in place (to alert themselves internally and to externally let the borrower know they were on the bank’s radar) to monitor, manage and control this situation.

    Seeing a lot more people then previously with high and low-LTV not making repayments should be seen as something serious broken in the banking system.

    Just as tellingly, with over 50% of SME loans in arrears, you have another sign that something is very broken in the Irish banks.

    Worryingly – you also have a glimpse of more holes appearing in books of the zombie banks – and now they have the “Cyprus” option…

  4. Fancy a NAMA house? Just pick an empty one, move in and claim squatter’s rights. No negative equity mortgage required
    …one solution anyway! D’ye remember?
    The engineering and architectural students in UCD that I am fortunate enough to engage with are always very amused at that particular solution to the housing and mortgage issue in Ireland.
    On a related theme: given the current media coverage on Priory Hall, would not the PR consultants engaged by KBC Bank be well advised to ‘pull’ their current advertisement about caring etc.

  5. There are many solutions readily available to the residents of Priory Hall who have had to endure undescribable torture due to inaction of: Banks, Architects, Local Authorities, Builders and Politicians.
    The death of a young father with two small children campaigning for justice in this inner circle of hell not of his making is a call for a solution.
    It really is not very difficult. There are many good properties available at Northern Cross. I just walked the site…again. All that has to happen is that people get a key. They move in and turn the lights on.
    A sleight of hand in the Dail could make it happen.
    Failing this, people could just quite simply move into those properties which are habitable.
    Is there any person in Ireland or a court of law who would evict a person under these circumstances?
    It’s just a thought…

  6. David Duffy said that strategic arrears for AIB were around 2% at the recent Dail Finance committee. Gregory Connor has been an inexplicable, shameless, cheer leader for spreading rumour after rumour figures on the level of “strategic defaults”. Why did PTSB not turn up with their sob story in the Dail 2 weeks ago?

    Mr. O’Connor you are wasting a god awful amount of time mining an anonymous data set. You want to tank them for the anonymous data set so do I because I don’t believe in anonymous data sets. This is a state entity and they should not be leaking any data sets to anyone the whole lot should be out there in the open published for all and sundry to analyse. Basically, I just want one figure, how many mortgages that PTSB have out of their total mortgage book are “strategic” defaulters. No mumbo jumbo no funny stuff professor? Oh and it might help to get a clear definition of “strategic defaulters”. The definition is the goal post that keeps being moved around.

    Alan Dukes tells us the banks have not got a clue about what the losses on their residential loan books are going to be buy you can dice and slice into that loan book to tell us what the “strategic defaulters” are? Now if we know what the motivation of the strategic defaulters are please Sir pray tell what is your motivation, your obsession if you will, with “strategic defaulters”?

  7. RB
    stall the ball there. Then play it and not the man.
    Gregory is doing sterling work tick tacking with the issue. Nobody knows nuttin yet. Any and all light is useful.

  8. @Brian Lucey — I divided the intercept into a PPR dummy and an “other” dummy which add up to the intercept. So the weighted average of their coefficients equals the coefficient on the constant term. This is the well-known “dummy variable trap” that you cannot have a full set of dummies and a constant term. So I left out the constant term and used two dummies which seemed clearer to interpret?

    Note that the sample consists only of mortgages which have submitted an SFS, so it is not all mortgages. That is why the proportion of defaulted mortgages (within this restricted set of mortgages) is so high. I might go back and edit the text slightly to make that clearer and thanks for the comments.

  9. Robert Browne – “anonymized” just means that any personal identification data has been stripped out. That is standard procedure for social science research. But they have promised us that it is clean and complete to the extent feasible.

  10. @Gregory Connor,

    Thanks for this.

    Looking at fig. 1 (and I may be reading it wrong), why does it peak before the end? This would seem to imply that a huge number of mortgages with an LTV of 2.8 are defaulting but that this declines pretty steadily thereafter. Should it not continue to rise if LTV is the major factor in driving arrears?

    Thank you for your time.

  11. @Chris Short — There is often a boundary problem with kernel estimates since they become unreliable at the edges of the data range. Here there is another problem since mortgages with current loan-to-value ratios that are extremely high may have a high proportion of data errors. So the answer is I do not know but I am not surprised that the curve gets a bit wobbly out there.

  12. one thing we need to be clear on : Guiso et al DO NOT LOOK AT STRATEGIC DEFAULT.
    “To identify the proportion of strategic defaults, we employ two questions. The first asks, “How many people do you know who have defaulted on their house mortgage?” Those who know at least one such person are then asked, “Of the people you know who have defaulted on their mortgage, how many do you think walked away even if they could afford to pay the monthly mortgage?” By taking a ratio of the two, we obtain an estimate of the percentage of actual defaults that are considered “strategic” by the defaulters’ acquaintances. ”
    This is, I content, at best a most imperfect fuzzy and eminently caveatable measure. We dont even have that here.

  13. “Current loan-to-value has no effect on a household’s ability to pay the mortgage”

    That statement is true, but does it really imply that current loan-to-value should not be correlated with default, in the absence of strategic defaulters?

    Current loan-to-value in Ireland will presumably be highest for mortgages obtained during the worst years of the bubble, at a time when credit standards were poor and banks were willing to lend to anyone with a pulse. The people paying these mortgages will tend of a certain age, and other studies have shown that the recession and austerity have affected certain age groups more than others. Are these not factors that could produce a correlation between current loan-to-value and lilklihood of default, even in the absence of strategic defaulters?

  14. I have read this blogpost several times but I am still finding it difficult to decipher. Is there a split between PPR mortgages and BTL mortgages? It seems to me a mortgage holder is more likely to submit a Standard Financial Statement for a BTL. Many might see these as deeply underwater and would be glad to get rid of them having no emotional attachment to them unlike a PPR. Some recent posters have also asked if the figures on BTL mortgages with/without personal guarantees are available. This seems to be an important piece of information although Permanent TSB are unlikely to divulge that information given it might shed unwanted light on their mortgage underwriting during the boom. Do we know how many BTL’s that are in default are still being rented with nothing handed over to the bank?

    As someone who purchased a BTL during the boom but had to flog it a short time later due to financial circumstances, it seems to me that strategically defaulting on a BTL even where a personal guarantee had been given would be an entirely logical decision.

  15. Totally off topic but of interest to Dublin academics.

    “She was consumed with family above all and spoke often of her fondness for her Irish grandfather, Michael Monaghan, who lived in Quebec City and with whom she corresponded in Latin. She proudly related that though he taught at Trinity while in Dublin, he also had to drive a milk cart in order to adequately feed his family.”

  16. We’ve handed over billions to bankers who we know now were clearly gaming the system – all the while they kept their jobs and earned millions.

    And yet we’re still, even now five years on, worried about some punter getting one over with a “strategic default.”

    It would be like inspecting people’s shoes as they boarded life boats on the Titanic – “no hard soles people, you might scratch the side of the ship.”

  17. The Prof should get used to being criticised: no one wants to know! Irish solution to an Irish problem.

    Except it is inherent that strategic default is merely a mirror of the Pyramid scheme that suckered these investors. Reckless lending is always the correct description of the last lending before a crash. How many times have we seen this? How many more times will we see it? Having hard evidence that the state was so heavily involved is a little unusual, but then we have the French Monarchy.

    Truly Darwinian: red in tooth and claw? I am quite amazed at how supine the Irish are? Suicides by the score, but no murders of those responsible? We must keep up this focus on the deceived, amateur investors and not the professional, knowledgeable bond holders who organized the whole scheme, possible once low interest rates were imposed.

    The search for the guilty and the punishment of the innocent!

    What a farce! What Comedy? It is a wonder that the Greeks are not flooding into Dun Laoghire…. Maybe the Bulgars and Romany will give them a lift?

    The borrowers are to blame ….The borrowers are to blame ….The borrowers are to blame ….The borrowers are to blame ….The borrowers are to blame ….The borrowers are to blame ….The borrowers are to blame ….The borrowers are to blame ….
    The borrowers are to blame ….The borrowers are to blame ….The borrowers are to blame ….The borrowers are to blame ….The borrowers are to blame ….The borrowers are to blame ….The borrowers are to blame ….The borrowers are to blame ….
    The borrowers are to blame ….The borrowers are to blame ….The borrowers are to blame ….The borrowers are to blame ….The borrowers are to blame ….The borrowers are to blame ….The borrowers are to blame ….The borrowers are to blame ….

  18. Any attempt to measure ‘strategic’ defaults is to be welcomed, because undoubtedly there are strategic defaults. A few points.

    The word delinquent, while used in the US for late payments of all kinds, carries a much more pejorative meaning, currently and historically, in Ireland and the UK, where its meaning generally denotes repeated criminal offending.

    The data would appear to suggest that even where ‘just’ 30% of net income is used to service the mortgage, up to 25% default where the loan/value ratio is high. This on first reflection is a very high figure. However what does it mean for different groups of income earner.

    Monthly net income Mortgage
    10,000 3000
    6000 1800
    4000 1200
    3000 900
    2000 600
    1500 450
    1000 300

    So, who is likely to be a strategic defaulter? It is abundantly clear that those > 4000 net monthly income should, prima facie, be able to afford the mortgage and still live. The same cannot be said at all for the person whose net income is 2000 or lower.
    Absolute net income is a ‘must know’ figure in relation to the evaluation of true strategic default percentages.

    The next point I would make about the data, is that unless one separates BTL from OO, then the data will lack any effectiveness form a policy point of view. Although lumped together, in a very bad error of judgement, in the Blackrock / PCAR exercise, they are entirely different from the point of view of society and it is society that is paying the cost of the crisis.
    They may all be PDH mortgages to the banks, but that is a bank definition. We need separation of these completely different mortgages when viewed by the individual or society.

    Jim Stafford, the leading insolvency expert, in addition to his remarks on professional versus paye housing requirements, mentioned a case on of his on radio the same evening.
    The person owed €40 million, his assets were his wife name and he worked for his sons.
    Strategic default?
    Make no mistake about to which income sector the vast bulk of bank write-off will go. Many have already gone there.

  19. If you rewrite the relevant paragraphs above – but look at the LTV issue from the bank’s perspective:

    “….. security recovery behaviour has been shown to be significantly affected by the current loan-to-value ratio of a property. Current loan-to-value has no effect on a healthy bank’s ability to enforce the mortgage, but it has a big potential impact on a zombie bank’s willingness to repossess. Current loan-to-value has no short-term cash flow implications (the bank will have to write down it’s loan book though) but it tells the banker his/her paper gain or loss on the leveraged property investment.

    For zombie bankers, repossessing a property deep in negative equity (high loan-to-value) is “wasted money” over the medium term since the capital loss is too big to be reversed by random price changes. Zombie banks are very sensitive to current loan-to-value whereas healthy banks (those who repossess) are completely insensitive to current loan-to-value.”

    When your arrears get to 14% of your loan book – is that a sign of a healthy bank or a zombie bank?

  20. The mortgage cirsis shows how a society’s poltiical, legal and financial institutions can struggle to function when there is a widespread problem of bad debt. Ireland’s prior laws around bankruptcy and reposession were quickly acknowledged to be inadequate, but our politicians have done little to improve them despite several attempts. Our courts are laboring under a heavy case load and could face a deluge if the banks actually went after every delinquent mortgage. However our banks have shown little enthusiasm for ths task, even though they have been handed several billion from the government expressly for the purpose.

    Under these circumstances who can doubt that the percentage of strategic defaulters is greater than normal. But the roots of the crsis are not in strategic default, but in institutional stress and failure in the face of widespread over -indebtedness.

    The processes of building up debt, and then removng bad debt through default and restructuring, are not symmetric. One is easy and pleasant, the other difficult and painful. The mantra “Debt doesn’t matter, because one man’s debt is another man’s asset”, which implies symmetry, is false.

  21. I’m with Elia – any strategic default I have seen has been mostly BTL. In my experience the majority of owner occupiers try and pay their mortgage. Those who cant just want the certainty of being able to stay in their family home and I think would be willing to pay a price for that, possibly in terms of a swap of debt for future appreciation. John Hussmans explanation (which I have linked before) of how this might work is still the best that i have read – four years on….

  22. Prof Eamon Walsh gave a balanced response to the Oireachtas hearings in an RTÉ Morning Ireland interview:

    What is striking about this issue and so many more that are highlighted in the OECD survey of Ireland, is the staggering level of managerial incompetence in Irish institutions when it comes to process.

    People run from hard decisions and for people like Richard Bruton running a permanent publicity campaign, it must seem a lot more exciting than trying to sort out the apprenticeship shambles; the innovation shambles and the banjaxed job activation programmes.

    In the case of the mortgage and SME debt crisis, the Central Bank appears to operate by target when it should be in charge and shaming ministers to update laws that are hindering resolution of the mess.

    Eamon Walsh said some banker had said a customer with money on deposit was not paying a mortgage with the bank.

    That may be an isolated case but do not doubt that the system is shambolic.

    There is nobody in charge.

  23. @Gregory,

    Might the data set have variables other than age that correlate with loan to value ratio? I’m thinking variables like occupation, sector of employment, location, current employment status …

    I think an important aspect of strategic default in the US is that many mortgages are non-recourse. Once the loan significantly exceeds the property’s value, borrowers don’t have much to lose from defaulting, and mortgage providers potentially lose a free property caretaking, maintenance and value-of-neighbourhood-preservation service if they reposess. Strategic default can be a practical way to achieve a positive sum outcome for the two sides.

    Ireland is, at least theoretically, different, in that the mortgage and arrears will continue to follow the home-owner around in case of repossession or jingle mail.

  24. @ BeeCeeTee

    Based on information compiled by the National Consumer Law Center (NCLC), at least 10 states can be generally classified as non-recourse for residential mortgages: Alaska, Arizona, California, Hawaii, Minnesota, Montana, North Dakota, Oklahoma, Oregon, and Washington. Recent legislation also makes Nevada non-recourse in most cases for residential purchasers for mortgages obtained on or after October 1, 2009.

  25. @MH,

    Thanks for that. I think it is worth observing that many additional states heavily limit recourse, while still being treated as recourse states in that 10/11 state summary. For example, New York limits recourse to the fair value of the property.

  26. This is senior hurling. When a crisis overtakes the ability of an industry to self manage, it becomes political. Fukushima.

    This bank is regulated by the Financial Authority. Maybe it wasn’t.
    Your home is at risk if you do not keep up repayments. Maybe it isn’t.

    That old economics stalwart, the rational agent- what would he do ?
    And who is going to pay for it? And what does Joe Duffy’s woman in Clontarf make of it all ?

    And all the time the house prices fall.

  27. Terrific excellent work,can’t argue with the math.Assume FICO scores or “credit number” na.
    Not a clue on Irish data tapes,but shurly a high “FICO” would be indicative off a chancer.
    How reliable are the LTV’s,in house or benched from date/vintage of origination.Are they revalued after default by drive by?

    In Cali only purchase money borrowing applies,cash outs say for holliers,updating the mobile home allow a deficiency judgement to be pursued.

  28. The crude assumption here is that there is a clear distinction between can’t pay/won’t pay. The only people who genuinely can’t pay are those who do not have the money. But most would also include those who don’t have the money left after paying for “necessities”. What about those who don’t have the money left after paying for Sky, the second holiday, the second family car etc. Paying the mortgage takes its place in priority for the discretionary spend. It is entirely to be expected that that priority would fall down the list as the payments are perceived to be more and more money into a black hole. Gregory seems to define strategic default as anybody who has not pared their expenditure back to the bare necessities. For me truly wicked strategic defaulting is when the money is actually diverted into savings and I don’t think there is evidence here that this is happening to any great degree.

    Also I think skeptic’s observation that LTV may be a proxy to completely different risk factors such as belonging to an era of reckless lending or pertaining to loans of recent vintage greatly undermines the inference that the statistics are mainly explained by strategic default.

    I won’t pretend to understand the probit/logit stuff, maybe I have to go to Limerick for that.

  29. @BWII

    The lowest of the low are the BTL landlords who fund their lifestyle from the rent and default on the mortgage. And STILL the banks won’t repossess. That is not just incompetence, it must reflect a deliberate policy on the bank’s part (or their masters) to support the housing market.

  30. @seafoid

    Joe Duffy’s ‘woman in Clontarf’ is delighted to tell you that your reference to house prices still falling does not apply to Clontarf!!

  31. not sure if i linked these before few yank bits and pieces,its Friday lunch time,don’t ask please,but yep i did read them….
    to paraphrase Fitzgerald..’the yanks are different from you and me’ but the math and yardstick’s used are somewhat mildly interesting….like if you have absolutely nothing better to do.In which case you really need to get out more…

    pretty sure i did not link the MS paper

    the rand not so sure,tried the ‘search’ on ie drew a blank.

    anyway enjoy !

  32. @ Gregory Connor

    After a crash course on probits I am struggling with your figures. As I understand it the probit beta for LTV is .3983. So if LTV goes from 1.5 to 2 that would be a shift of .1995 sigmas but that can never give rise to as big a shift in probabilities as 19.92% unless you mean this is the percentage shift in the probabilities e.g. from 10% to 11.992%. What am I missing?

  33. @Brian Woods II — Thanks for that! — there was a missing normal distribution term and I fixed it —see W.H. Green Econometric Analysis Section 19.3.1 in particular equation 19-10. I just took a first-order Taylor approximation, as is standard. It is not exact.

  34. @ Johnny Foreigner

    I know self-employed tradesmen and others on incomes less than €50k who were buy-to-let investors or who even bought apartments abroad in the belief it would provide them with a pension fund. Michael Hennigan regularly posts here on the poor pension coverage in the private sector. A colleague in work from several years back who had started her first pensionable employment in her early thirties bought a 3-bed BTL in a regional town and called that her ‘pension fund’. Subsequently she married and had two kids but last year she and her husband, who lost his job in the construction sector, and the kids emigrated to England where he had found work. I’ve no idea if her 3-bed is rented out but if it is and she’s not handing over the rental to the bank … well, as Pope Francis might say, who am I to condemn her? What does she and her family owe Ireland Inc?

    The use of the words ‘fund their lifestyle’ is pejorative. What if withholding rental payments from a bank is being used to pay for school uniforms or doctors bills for those ‘small’ investors. Many BTL’s in regional towns may be renting at only €500-€800 per month if tenants are found.

    I’m not so naive to believe there aren’t very wealthy people who are gaming the system and will be well-placed to get a write-down of their mortgage but, in the rogues gallery of those responsible for the current mess, I would put BTL strategic defaulters down the line a bit.

    By the way, I enjoy your posts on here so please don’t take this personally.

  35. It is not clear that there’s enough information in the dataset to clear the mist on strategic defaults . Any chance of age, location, original salary, current salary, year of purchase , fall in property value, value of savings with banks ?

    The banks have all the data and it seems they are releasing it selectively.

  36. @Elia

    Let me get this straight… you’re saying that the landlord is 1) right to not repay the bank and 2) steal from the tenant – am I reading you right?

    Most people don’t understand buying assets, or investing in pensions, using leverage. Leverage is your friend when prices are rising – but it magnifies your losses when prices fall.

    Putting only 10% down and effectively gambling that the income stream and/or capital appreciation will cover the remaining 90% is a risky 20-year strategy – but people don’t seem to see it that way!

    The BTLer/”investor” is legally bound to meet his/her debts as they fall due. If they fail to do so then they must accept that they should lose the asset and make good any shortfall. In a falling market this is where leverage wipes out the “investor”.

    For that “investor” to then turn around and divert an income stream intended for the bank for their own purposes, is theft.

    So the BTLer is both a thief and a deadbeat but still worthy of your support… Is that really what you’re saying?

  37. @ WGU

    I can’t see how you formed that view from my post. I merely said I wouldn’t condemn those who bought overpriced property in an attempt to create a pension fund for themselves and then, as a consequence of personal circumstances, decided to prioritise the rental for necessary living expenses. Good luck to them while the banks dither on repossessing. No tenant is discommoded: he/she enjoys the use of the property while paying a monthly rent and he/she is not to know who the ultimate owner is of the property. If you choose to call these people “thiefs” and “deadbeats” so be it. All I’m saying is I don’t condemn them. As Mrs Slocombe used to say (‘Are You Being Served’): “I am unanimous in this”.

  38. @Elia

    Your rationale seems to be that it is ok to do pretty much anything in the name of preparing for old age? I could use the same reasoning to simply rob a bank. It’s stealing from the bank, but all in one go rather than stretched out over a long period.

    People who aren’t paying their mortgages are squatters. I actually have a lot of sympathy for squatters but let’s treat them all the same way. If a homeless person decides to squat in an empty property owned by a bank I want to see the bank treat that person in exactly the same way as someone who isn’t paying their mortgage.

    What is maddening is the financial system arbitrarily picking winners and losers in a way that seems completely detatched from the normal system of rewards for economic behaviour. Why save or delay gratification in this country? It’s just an invitation to be ridden from here to eternity.

  39. @ Gregory Connor

    Thanks for that clarification. I have put te probit parameters into excel and looked at a few of the marginal distributions. By and large the model directionally is in accord with our intuition but I think if we stray far from the median the linear nature of the model lacks credibility. For example, setting PPR=1, NONPPR=0,LTV=1, APPNETS = .2 and examining the marginal distribution of NETS we get a Pr(def) = 33% when NETS = 0 and Pr(def) = 54% when NETS = 1. It seems that some transformation of NETS to a variable ranging from -inf at NETS=0 to +inf at NETS = 1 would be more credible.

    I realise it is easy to knock any model so being more constructive I looked at the LTV marginal distribution with NETS = .2. This constituency could perhaps be characterised as those who could pay their mortgage of they made a reasonable effort and I also think any inferences about them are less susceptible to skeptic01 syndrome.

    This graph clearly demonstrates that the probability of default increases significantly with LTV with the 50% Pr(def) occuring at 1.85. At this value the people in the survey are most likely to make the decision to switch from making the effort to pay their mortgage to throwing in the towel – that seems reasonably credible.

    As mentioned before I hesitate to use the pejorative term “strategic default”. Better to say that the more your property drops into negative equity the less sacrifices you are prepared to make to pay down your mortgage. True strategic default is when with little or no sacrifice you can pay your mortgage but have decided not to do so, possibly saving to make a moonlight flit out of the country.

  40. @Brian Woods II — I was thinking about that “nonlinearity” evident in the effect of loan-to-value on defaults and actually was just doing some analysis earlier this morning of that. I found the local average probit-based expected default and the local-average empirical default, where local means in the neighbourhood of a particular level of loan-to-value. The difference between these two is the unexplained, nonlinear relationship between empirical average defaults and multilinear probit model predictions of default. (Sorry this is a bit wonkish to use John McHale’s word). I will see if I can make the graph work by putting it in dropbox.

  41. I love the definition there BW2. Its useful and sensible. Far more so than characterising those in arrears as squatters.

  42. @ Gregory Connor

    Yes that graph works. Just to make sure I understand it. The red line is not quite straight because you adjust for other local probit parameters. The blue line touches 1 which means that in that locale everybody defaulted. I am a bit surprised that you have data in the locale of LTV=0 and even more surprised that the enexplaind in that locale is positive or in absolute terms the default in the locale of those with negligible LTV is greater than 40%! I think this highlights the caveat which you stress, this sample is of those who have (a) got into trouble and (b) filled out the form. And while we are here I am amazed that PTSB have over 30,000 souls in that category.

  43. The kernel estimator find people in every local “neighborhood” so if there is no observations with LTV near zero it will use observations with LTV as close as possible to zero. It weights the observations according to how far they are from the target value.

    The red line is not quite straight since it is a multi-variable linear model but this is a salami-slice which only sorts based on LTV and the other explanatory variables differ in their average values as LTV varies.

    The sample consists only of mortgages with SFS documents so it is only troubled or near-troubled mortgages. I am not sure if anyone would submit an SFS otherwise — unless perhaps they have both OO and BTL mortgages and have difficulty paying the BTL even though the OO is completely untroubled. There is a large category called “multiple” for individuals with multiple loans.

  44. @ Kevin Lyda,

    Define the word “bankers”, because lots of people who “just so happened to work in a bank” have already lost their jobs. Perhaps you mean the upper echelons of management.

    In relation to the defaulting of the BTL sector. The Govt has implemented “Taxation on a loss” measures to which the Revenue are only too happy to implement.

    In my estimation… for a landlord to receive less than 800 euro / month it is just not economical, the LL will lose money and is unable to cover the costs of providing the service. Hence it is all but inevitable that some LL’s will not return money to cover the mortgage.

    BTL sector only works with rent close to and in excess of 1000 / month and mortgage costs being zero or very low.

    I estimate… that for an apartment renting at 1100 / month, there would be at least 3K to 4K in costs alone per year and this is not including mortgage repayment costs.

    BTL loans today are at least 5%, ranging up to 6%.. God help investors when the ECB starts to raise interest rates in a few years time.

    For any investment… if the costs exceed the return… it’s not economical.
    If the return is far less than the costs… then its not economical either.

    As for Strategic Defaulters…I could well believe this… there is NO shortage of chancer’s and thieves in this country. Robbery is not related to one particular class either, all classes of society are at it.

    I have spoken to various shop owners, garden centers etc… and they are all suffering heavily from theft, and they all say the same thing… it’s not just lower classes of society thieving… it’s all classes.

  45. @Brian Woods II – I think that you are misinterpreting why the “unexplained” graph goes up at low LTV. The linear model is forced to split right down the middle with a straight line. If there is a nonlinear upward effect at high LTV, then the linear model is forced to partly account for it and therefore it gives an offset at low LTV also going up. So the upward bump of the unexplained component at the low end is an artifact of fitting a linear relationship to an effect which has a nonlinear upward curve at the higher end.

  46. @ Gregory Connor

    I have to think about that a bit more. Meanwhile I am going to try your trick.

    Does this spreadsheet (presuming you can open it) correctly interpret the model? Actually it is surprising the lines are straight at all since they are inverse normal distributions but it seems that over the limited range the PDF of the normal distribution is roughly constant.

  47. @ Gregory Connor

    I am indeed confused by the unexplained. You describe your blue line as the “local-average empirical default”. I took “empirical” to man the actual observed default in that locale, which I was surprised should be so high in the locality of negligible LTVs. Am I misinterpreting the meaning of the word “empirical”?

  48. @ Prof Lucey

    Obviously if the death penalty was introduced for defaulters or, more realistically, banks became more aggressive in pursuing them then the default rate would fall. To therefore categorise the extent of the absence of that fall as a “strategic” decision rather suggests more Machiavellian intent than is justified.

  49. @Brian Woods II — I see the empirical graph as essentially flat for LTV less than 1. The minor bumps are just noise. Above 1 the relationship slopes nonlinearly upward with an upward curve. Fitting a straight line through that empirical data gives a line which will underfit at the top end and underfit at the bottom end. So the lower end “underfit” is just an artifact — at low LTV default has the same flat constant value as it does at LTV=1 but the linear relationship gives a worse fit at low LTV.

  50. @ Gregory Connor

    Actually that makes perfect intuitive sense. These people have got into trouble. At LTVs below 1 the LTV is not a factor – something else has put them into difficulty. Emhasises again that we must be constanty aware of the selected population we are studying – those who got into difficulty.

  51. @ Gregory Connor

    It seems one should try and subjectively come up with potentially better fits than linear. For example, it would seem reasonable to posit that for LTVs below .9 the LTV is not factor. This might suggest a better variable is -inf up to LTV=.9 and log(LTV-.9) for LTV>.9. Similarly we might try log(NETS/(1-NETS)). The test of success would be whether you increase significantly the max log likelihood.

  52. Proving a relationship between LTV and default doesn’t really tell you much about strategic defaulters. IF LTV 100, while an LTV of 110 implies a small, but not zero, chance that true LTV < 100. Even if you had income data, the concept of “strategic default” is murky. If someone sees their income fall by half, and they have enough income to make the house payment OR the car payment, but not both, and they make the house payment when equity is positive, but the car payment when equity is negative, are they a “strategic defaulter?”

  53. Very interesting discussion. Maith sibh

    Samuel Karlin was supposed to have said “The purpose of models is not to fit the data but to sharpen the questions”.

    I wonder what the influence of the individual bank is on the level of defaults. Which bank has the biggest share of the post 2005 business, the stuff most likely to be in trouble, as a % of total mortgage book ?

    ILPM grew very aggressively pre 2008 and they probably weren’t expecting prices to fall…In 2009 they told investors that arrears would peak in 2010 with unemployment .. as if..

  54. @ GC

    Correction to earlier suggestion. Obviously transforming the LTV variable to -inf below .9 would eliminate modelled defaults below that level irrespective of the other variables, so that is not right. Max(.9,LTV) though would possibly give a better fit than unadjusted LTV, from inspection of your graph.

  55. hmm – less than signs came through in my post, but greater than signs did not. I was trying to say that if LTV is greater than 100 you should default if the face of a hit to cash flow, and with LTV less than 100 you shouldn’t. And a measured LTV of 110 means thaere is a small, but non-zero, chance that true LTV is less than 100.

  56. @an duanaire

    Minor point: Colm McCarthy did ‘not’ invent austerity.

    Austerity was invented/created by the 2002-2007 admin steeped in the ‘efficent markets hypothesis’ (sic) ideology of the Progressive Democrats in bed with a reckless Fianna Fail cabinet – the inventors were Michael McDowell, Mary Harney, Charles McCreevey, a silent Brian Cowen, and Bertrand Ahern.

    … hence this thread on the misery of thousands.

    Keep up the good work.

  57. @John Gallagher — Thanks for the Morgan Stanley report link. Their results are similar to ours — Exhibit 6 in the paper looks Figure 1 in my blog piece above (but my econometric technique is more cutting-edge!). And their summary point sounds like one of the points of the blog piece:

    “At low levels of negative equity, strategic defaults are relatively low but they pick up steadily as the degree of negative equity

  58. @Gregory Connor

    Whatever the ‘cutting-edge’ nature of the econometric techniques the plausibility of the findings depends on the underlying quality, and limitations, of the data set.

    That said, the move to some empirics in the Irish context is welcome.

  59. fyi
    Struggling families with no assets won’t get debt deals

    BROKE families that have no income and no assets they can sell off will not be able to avail of the new state-backed insolvency deals. Head of the new Insolvency Service of Ireland Lorcan O’Connor revealed that these people will have no option but to declare themselves bankrupt.

    Mr O’Connor’s admission will further perceptions that the new Insolvency Service has been set up mainly to benefit the professional classes, and is not for PAYE workers. […] And anyone seeking a PIA or a DSA will have to find at least €5,000 to pay a PIP to propose a deal to their bank for them.

  60. @ GC

    WARNING this post is unashamedly wonkish.

    I did my Wiki/Google bit on kernel estimation. What I read is that it is an estimation of a p.d.f, a sort of continuous histogram.

    You have use “kernel-based” techniques to fit the default ratio as a function of LTV. This is not a p.d.f. I presume the answer is in your qualification of kernel with “-based”.

  61. Brian Woods II — kernel methods can be used to estimate density functions or any other smooth functions. Density functions are a common use but not the only use. Here, kernel methods are being used to estimate expected default as a smooth, univariate function of loan-to-value.

  62. @GC
    Table 1 seems to have arrears of sub 40% for the sample but figure 1 shows the arrears rate as around 40% and up for most loan to value ratios, including those in positive equity. How much data is each group that Table 1 based on?

    If you ignore all <30%, then the picture isn’t as clear. The significance of the 2 binomial models does show that LTV is significant but an R squared of .06 seems quite low to me.

    I’d be very interested in a model which adds variable rate and tracker rate dummy variables to the models as I think this could be a big driver of the affordability ratio.

    You say that there is no relationship between arrears and LTV, as arrears is based purely on cashflows. However while a morgage holder is in arrears, the LTV is increasing driven by the increase in the principle loan amount for the arrears. Looking at the Q2 central bank data, 20% of Total arrears are over 2 years in arrears and 20% between 1 and 2 years. This probably wasn’t as much of a problem in the US data.

    I also wonder if the dataset contains some informative censoring, as more sustainable solutions – eg. term extention – would be offered to those who have low LTV ratios by PTSB. Are restructured morgages in the data? How?

    It is good to see analysis of the massive problem that is morgage arrears in this country – be it strategic or otherwise.

  63. The MS paper linked above cross references another paper titled “Forgive and Forget” in the interests of completeness here is link.Given the correlation btw. NE and SD,the dearth of foreclosures and lack off political will in Irl.Perhaps motivate them to pay…..

    “Many options, little will. Many policy options are available to fix America’s dysfunctional housing and mortgage markets. But the political will to deploy them is scarce. Small wonder: None is a panacea, most reward ‘bad’ behavior, some involve government funds, and none will satisfy all parties. Yet all are better than doing nothing, and a combination of carrots and sticks could create incentives for good behavior and real results.”

  64. so, the next logical step would be, to draw 2- or 3-sigma confidence bands around the curve in figure 1.
    What program do you use?

    Thanks to the posting of the financial statement by brian woods snr, it looks feasible to me, to analyze for the income remaining for consumption, divided by family size (the SOEP / DIW counts 1st adult 1.0, all others 0.5, and children 0.3 – 0.5 as “effective consumption weight”, not their phrase!)

    My expectation is, that this goes a long way to explain non-strategic defaulters, expecially those with LTV ratios< 1.0, which would then also help understanding at higher ratios.

  65. @ BW II: I had a good chuckle at that! Nice to be ‘confused’!

    @ francis: I’m the scientist – my namesake BW II is, I believe, an Actuary. So he will be good at the math stuff.

    My ‘stuff’ is fossil energy sources and their relationship to various aspects of economic activity.

  66. Oooops,

    I am very sorry, and I like you both : – )
    Sometimes I am digging around in fossils like Wilhelm Röpke 1932 “crisis and cycles” myself : – )

    first bavaria prognosis 57 % of the seats for the black block CSU, the greenies are cratering and already a big mouth

    18:00 49 21 8.5 3 2 8.5 2.0 6.0 projection
    18:23 49 20.9 8.3 3 2.1 8.4 8.3 first counts

  67. @seafóid

    “The banks have all the data and it seems they are releasing it selectively.”

    That would be an accurate statement.

    Blame the borrowers. Blame the borrowers. Blame the borrowers.

  68. Gregory,

    I don’t see how you can glean the extent of strategic default from this analysis. You are missing data on ability of the person to service the loan. Given the nature of the Irish property bubble and subsequent collapse, it is entirely possible that the loan-to-value ratio is correlated with characteristics of the mortgage holders that would be related to ability to pay. I dont see how the estimation you perform rules out this unobserved correlation. It would be worth displaying the marginal effects from the probit model. As Brian points out above, in the absence of characteristics of the borrowers, you are effectively assuming no correlation between LTV and other adverse borrower characteristics. I don’t see how that assumption is at all justified and your cofficients may simply be picking these up.

  69. Sorry, just to clarify my point I am aware that you have measures of income both at time of mortgage and current time. But loan servicing ability is also a function of other expenditures. For example, a correlation between number of dependent children and LTV could explain your results. I am not suggesting that explanation in particular but it would certainly be neccesary to argue why the error term is unproblematic in this model before using the marginal effects as indices of “delinquency”.

  70. @Liam Delaney – We have looked at some of these alternatives but it gets overwhelming quite quickly. Working backwards from LTV it is a nonlinear function of five or six variables, which in turn are nonlinear functions of five or six variables each, so it turns into a horrible mess with about a hundred or so variables explaining why default might be linked to LTV. This does not include the number of dependent children, which makes 101 variables. I am not sure what number is the potential combination of 101 variables. It seems simpler to stick with the one-variable LTV which has good support in the existing literature, but none of the 101-variable combination alternatives can ever be ruled out categorically. The simpler model seems better from a social science perspective.

  71. @ GC: You are not achieving any positive result with this ‘research. If the input data is as iffy as you suggest, then you should have by-passed it. Pandora’s Box?

    Stepping back from the salient fact – that lots of folk are not servicing their debts (inc. mortgages) on time, there is/are causal factors for this situation. What is/are those causal factor/s?

    The first (and obvious one) that comes to mind is inability to pay; these folk are basically insolvent – their income/s is/are less than their expenses. So the first matter that has to be resolved is that of incomes – both total and nett. I doubt that any SFS form filling will achieve this. Maybe a mandatory Declaration of Income to the Revenue – with a pretty sharp ‘or else’ clause would, but again one has to wonder mightedly. Folk can be quite economical with the facts when it comes to ‘statements of income’.

    LTV ratios (Irish ones) are a quite hopeless metric. They have more in the way of a sentimental value as opposed to a quantitative value; a value that is appropriate for estimating a reliable statistic. You do know about that Meaningless Mean?

    No amount of statistical jiggery-pokery analysis will ‘straighten out’ bent or fraudulent input data. Its not the formulae – its the critter that selects the raw data and whether or not that raw data was sampled in a statistically robust manner. ???

    If I had proffered this analysis to one of my tutors, I fancy I might have got a flea in my ear and at best been instructed to re-do my analysis – using verifiable data – of a statistically reliable sort!

  72. @Brian Woods Snr — The input data seems ok and certainly not bent or fraudulent. That was someone else who said that — someone (I suspect) who wants to make sure that there are no findings that do not suit their political priors. When empirical evidence is politically unappealing it will never be accepted by many people. Political priors can have a big influence on people’s willingness to look at data — if this was about fruit flies or mixing chemicals the findings would be accepted easily.

  73. Gregory
    Two issues arise
    a) availability and b) use of data. What data are available to you? Thats one q. Then there are lots of techniques to engage in variable dimension reduction. three that come to mind are PC analysis, some form of stepwise regression, or a quasi Hendry type General to Specific approach. you have 30k obs. Degrees of freedom are not a problem
    In fact, this is really not the way to go imho. What would be useful would (variable dimensionality aside) be a nested LOGIT analysis from a universe of originated loans to see the determinants of full, stressed and partial (default) repayment. This dataset is censored in all sorts of ways and again we have no definition of strategic default.

  74. @ Liam Delaney

    I can see that there are plausible reasons for affordabiity to be somewhat correlated with APPLTV. Thus if one has pushed the bank manager to the limits of affordability you might also have pushed him to the limits of LTV. But there is no plausible argument for a correlation between the subsequent extent of NE and affordability (presuming that APPLTV is generallly <1). That is the most telling finding of the analysis, the fact that beta is significantly positive in the greater than LTV range. Certainly if it was cigarette consumption instead of LTV as the independent variable we would have pictures of distressed borrowers on cig packets.

    @ Prof Lucey

    You aiming for the prize of most wonkish post? I think I am slightly ahead.

  75. @BL,it’s starting to be reminiscent of Clinton,asking for a definition off sex,are you still in denial ?
    I think Gregory has done fantastic work,not for one minute am I pretending to understand all the “tech” parts,but I do understand strategic default,it ain’t that difficult a concept to grasp.

  76. JG
    No, but its damned hard to measure. And this is a small step. It may even be a misstep. Science advances slowly. Id prefer to get approximately right rather than exactly wrong answers.

  77. @BL it’s little old Ireland,at what “number” do you think policy will be impacted?
    Assuming there is any SD the logical next step is to review the policy options,too much stick is useless bit carrot may work much better.
    Motivate them to pay,see link above to “forgive and forget” or pretty much any decent research stateside on “fixing” SD.

  78. John I have no idea. I agree there are lots of approaches to deal with the mortgage mess. One is delay and pray which we seem to be doing at present.

  79. @BL doing nothing is extremely damaging to society,the situation is out of control.
    Brian if a massive humongous SD number overwhelms the court systems,then there truly is only one workable option left….shock horror debt write above.
    “Many options, little will. Many policy options are available to fix America’s dysfunctional housing and mortgage markets. But the political will to deploy them is scarce. Small wonder: None is a panacea, most reward ‘bad’ behavior, some involve government funds, and none will satisfy all parties. Yet all are better than doing nothing, and a combination of carrots and sticks could create incentives for good behavior and real results.”

  80. @Gregory

    I appreciate that it doesn’t make sense to go on a fishing trip adding in many variables that could potentially generate confounds. But there should be a middle ground between this and assuming that LTV is exogenous controlling for income. Even some simple things such as basic demographics would be easy to control for in the probit model without generating any computational problems. I personally would not accept your analysis at the very least without a good discussion of this basic econometric problem and, in fairness, you do flag that this post is a preview of the bigger paper.

  81. @brianwoodsII given the geographical pattern of house price reductions, are you confident that there is no reason for NE to be related to demographic factors?

  82. I always like to be the 100th posting, at time of writing I am in line

    @ LD

    Okaaay, still much more likely that increased NE is causal rather than a mere proxy to other factors. As a life assurance man we constantly come up across this conundrum – is a statistical risk factor causal or merely coincidental. The most controversial is treating gender as a rating factor. All statistical analyses point to gender being a mortality risk factor and yet the EU banned its use from last December.

  83. @Brian Woods 11-if anyone deserves it you do,terrific exchange of views excellent comments,thoroughly enjoying the exchanges,nice work.

  84. @Liam Delaney – My reluctance to jump into the swamp of all these potential second-order explanatory variables probably reflects my own financial economics background. In my own little niche of research we tend to use 1-5 explanatory variables maximum (obviously not in all models but in most). Big household panel datasets, such as in labour economics and such, are often analyzed based on fairly large numbers of explanatory variables each contributing just a little bit of explanatory power. I have not done so much of that type of work. I have done lots of empirical work with very large panels but they tend to be finance-type panels of asset returns and asset characteristics. This panel dataset is a “household finance” panel so it has both types of features.

    I am just looking for the big-picture influences and building a sensible model of these most important influences on default behaviour. Someone else can pick up the task of decomposing these big-picture influences into their myriad parts, hopefully, at a later stage.

    Incidentally, there is a large body of US research showing that LTV is a key determinant of strategic default, in the USA. See, e.g., Quigley et al Econometrica vol 68, 2000. People in Ireland do not seem so different to me that models of their behaviour should be unrelated.

  85. @Gregory thanks for response. My closing point is I agree with you that kitchen-sink approaches are not sensible particularly as if you keep putting in variables clearly something might come up as significant and correlated with LTV just by chance. What would be good to see in the paper is a review of what the basic econometric specifications are for loan defaults and, at least, an addressing of the potential omitted variable bias. Brian Woods II is arguing that the exogeneity assumption is not a problem. But I will read the full paper when it comes out and see whether any further light is shed.

    The Quigley paper is very relevant, thanks. As you say, they find support for your conclusions but their elaborations are interesting (quote below)

    We find that:
    1. The option model, in its most straightforward version, does a good job of
    explaining default and prepayment, but it is not enough by itself. Either
    transactions costs vary a great deal across borrowers, or else some people are simply much worse at exercising options.

    2. The simultaneity of the options is very important empirically in explaining behavior. In particular, factors that trigger one option are also important in triggering or foregoing exercise of the other.

    3. Unobserved borrower heterogeneity is quite important in accounting for
    borrower behavior. We allow for heterogeneity by incorporating into the estimation the possibility that there are different sorts of borrowers, some very astute, some quite passive, and others somewhere in between. We find that heterogeneity is significant. It has important effects on key elasticities explaining behavior, particularly with respect to prepayment.

  86. @Gregory Connor

    A number of questions arise from your dataset.

    The numbers the PTSB gave you:
    Did they segregate the BTL from the PPR?
    Did they indicate where on person had multiple mortgages in arrears?
    Did they show individual per-property arrears or simply show the LTV-to-arrears total?

    One person with a hundred BTLs in default with high-LTV is not counted as a hundred high-LTV in arrears, I assume?

    Also, having people fill out a SFS and selecting the data from this is a skewed pre-determined group – but not representative of the whole – of the arrears catagory, no? Those in arrears, but paying, with High-LTVs will not appear (if they haven’t sought or been asked to do a SFS yet) but those in arrears and not paying with high-LTVs will, no?

  87. @ GC: Note your comment. Thanks.

    ” … if this was about fruit flies or mixing chemicals the findings would be accepted easily.”

    Not by me they wouldn’t – I was a quantitative analyst! The quantitative (descriptive) statistical analysis performance characteristics I used were very nitpicky with respect to the sampling of raw data inputs. If you could not demonstrate that your entire measurement process was in a state of statistical control – you folded!

    Anyway, as you quite properly point out, its the purpose that the estimates are put to that usually causes the aggro. The boundary between verifiable knowledge claims and argumentative value claims is very thin. Most folk cannot think slowly about a complex problem.

    My comments are in respect of what conclusion/s the findings may/may not support. Attempting to estimate a reliable population parameter from a sample with an acknowledged bias is a very dodgy business indeed. Even if you clearly point out the defects in the raw data, non-technical folk will not drill-down through the data analysis and the results. They will go immediately to the ‘conclusions’ – then interpret them in whatever fashion best suits their own agenda. Trouble usually follows.

    The whole Irish residential mortgage mess is fraught with argumentative sentimentality. The idea that some naughty folk may be deliberately evading their mortgage debt obligations has a lot of other folk in a right royal lather; some on this site.

    @BW II: “All statistical analyses point to gender being a mortality risk factor and yet the EU banned its use from last December.”

    Pasteurized stats good, Eunuchized better!

  88. @Gregory Connor

    One other point on US research on “strategic” default – I would assume that the research was done in a situation where the banking system hadn’t implode.

    Do you think that comparing default rates in a system where the banking system continued as normal to default rates where the banking system imploded may be slightly misleading?

  89. Gregory
    I seem to be the designated referee (here my thoughts on that process btw
    Quigley et al state at the very end. “Finally, unemployment and divorce rates have significant effects on default”
    Et as they say, Seq.
    Gregory, Tom. There are so many missing variables that are shown in research to be also important in the decision that to go to bat on this data alone is not in my mind a good idea. Fuller data, if available, would be needed.

  90. @ Prof L

    “I seem to be the designated referee” on the evidence that would seem to me a self designation.

    Let’s get real here. All our intuition suggests that there would be a reduced willingness to pay off your mortgage the deeper you fall into NE. Anybody want to state categorically that they wouldn’t feel that way?

    The work done by GC on his dataset confirm this intuition beyond any reasonable doubt and also puts some plausible quantifiers on the effect. The cig industry still argues that cigs are good for you and the NRA are convinced that the availability of guns reduces gun crime. I hope this debate has been helpful to GC in anticipating the many possible criticisms that he will face. Most of the criticisms fall into the possible space but it seems to me much more plausible to accept that increasing NE is a prime causal factor in default (I decline to use the qualifier “strategic” for reasons explained earlier).

    @ JG ty

  91. @Gregory Connor,
    I have run an oul pencil over resi ‘tapes’,the ability to identify or estimate the SD’s in any pool is very valuable.With the banks/institutions flogging assets via ‘pools’ in Irl this work could be very valuable and useful in designing/selecting a pool to buy/sell.
    Now days no one wants to pay up front its all back end,i know i know,so the shorter the hold/stabilization period and exit the higher the IRR and naturally the fees-over here its know as ‘sweat equity’.You get paid after everyone else.
    SD defaulters have a few options to cure,you can hang around while they crank up the printing press,reducing the LTV or god forbid reduce the L in the LTV.
    Buyers off pools much prefer to deal with SD’s they tend to be more rational and less emotional,sorry to say but i don’t think the V in LTV in Irl is going to move much over the next few years.
    Fair play for making this initial work publicly available,looking forward to the full paper.

  92. We have drifted here. There is a vast literature (see some below) on the determinants of defaults. In many of these LTV is important. There is much less, due to nobody knowing what it is, on “strategic defaults”
    Here are some papers with extracts from the abstracts that suggest useful additional variables. If Greg and Tom have these then im sure they will include them. If they dont, then the paper can only be indicative of the importance of a set of bank selected variables.
    Below are papers, with extracts from the abstract. Their words not mine.

    Carranza 2013
    We show that home prices and debt balances are the main determinants of mortgage default.

    Quercia 2012
    even within moderate- and low-income segments, lower or very low income is associated with higher default and lower prepayment probabilities. In addition, depending on how low the borrower’s income is, classic determinants of loan termination such as credit scores, the amount of equity in the home and local labor market conditions can have different impacts on default and prepayment probabilities

    Sarmiento 2012
    This article shows that the rise in unemployment played a very significant factor in the rise of mortgage delinquencies during the Great Recession. Estimation results, moreover, show that changes in the Unemployment Rate (UR; from loan origination) as opposed to the level of the UR explain mortgage default.
    Crook 2012
    declines in credit quality for consumer and for real estate loans, but support for the reduced stigma explanation was restricted to real estate loans

    yang 2011
    mong the different volatility components, omitting the cross-sectional dispersion of individual home prices would produce the largest bias in assessing home-price-based mortgage default risk

    Kau 2011
    he paper demonstrates that MSA-level frailty, together with other risk factors, has significant effects on the probability of mortgage terminations risks.

    Pennington-Cross 2010
    Default probabilities increase dramatically when payment shocks are mixed with low or no equity in the home

    Seslen 2010
    using a novel measure, based on changes in net operating incomes and property values at the metropolitan statistical area-property-type-year level. Employing a semi-parametric competing risks model for a variety of specifications, we find that the probability of default is extremely low even at very high levels of stress, although the coefficient estimates of greatest interest are very statistically significant.

    An 2010
    he optimal choice between these two termination events may depend on unobserved propensities related to change in income, job location, or family size, and substantial inertial forces including search costs, neighborhood change and attachment to an area.

    Daglish 2009
    However, default probabilities are highly sensitive to changes in interest rates and house prices.

    Hagwouth 2008
    We find that while credit standards were important in determining the probability of an early default, changes in the economy-especially a sharp reversal in house price appreciation-after 2004 were the more critical factor in the increases in default rates that we observe. An important additional result is that in spite of our rich set of covariates, much of the increase remains unexplained, even in retrospect.

    Carranza, J.E., Estrada, D.
    Identifying the determinants of mortgage default in Colombia between 1997 and 2004
    (2013) Annals of Finance, 9 (3), pp. 501-518.

    Sarmiento, C.
    The role of the economic environment on mortgage defaults during the Great Recession
    (2012) Applied Financial Economics, 22 (3), pp. 243-250.

    Crook, J., Banasik, J.
    Forecasting and explaining aggregate consumer credit delinquency behaviour
    (2012) International Journal of Forecasting, 28 (1), pp. 145-160. .

    Kau, J.B., Keenan, D.C., Li, X.
    An Analysis of Mortgage Termination Risks: A Shared Frailty Approach with MSA-Level Random Effects
    (2011) Journal of Real Estate Finance and Economics, 42 (1), pp. 51-67.

    Yang, T.T., Lin, C.-C., Cho, M.
    Collateral Risk in Residential Mortgage Defaults
    (2011) Journal of Real Estate Finance and Economics, 42 (2), pp. 115-142.

    Pennington-Cross, A., Ho, G.
    The termination of subprime hybrid and fixed-rate mortgages
    (2010) Real Estate Economics, 38 (3), pp. 399-426.

    Seslen, T., Wheaton, W.C.
    Contemporaneous loan stress and termination risk in the cmbs pool: How «ruthless» is default
    (2010) Real Estate Economics, 38 (2), pp. 225-255.

    Daglish, T.
    What motivates a subprime borrower to default?
    (2009) Journal of Banking and Finance, 33 (4), pp. 681-693.

    Haughwout, A., Peach, R., Tracy, J.
    Juvenile delinquent mortgages: Bad credit or bad economy?
    (2008) Journal of Urban Economics, 64 (2), pp. 246-257.

    Deng, Y., Pavlov, A.D., Yang, L.
    Spatial heterogeneity in mortgage terminations by refinance, sale and default
    (2005) Real Estate Economics, 33 (4), pp. 739-764.

  93. @BL even mentioning/linking subprime borrowers in above devalues your contribution,its an oxymoron -ya think they SD then they ain’t subprime borrowers.

  94. Brian Lucey — There is a huge US literature that the authors think is about strategic default but I know that you feel that they are wrong and actually these papers are not about strategic default. But that is the word that the authors of these studies use repeatedly.

  95. Greg
    And not a one of em has a definition that we can work with here. Again that is the bedevilling issue. What you find is great – it confirms other research. But it is not about SD. Its about D. It may be about SD , but we need a whole pile more information before we can say that. Absent details on the dataset you have, and how this relates to what the banks have, its hard to see how we can progress this debate.

  96. Last post on this : From
    Luigi Guiso, Paolo Sodini, Chapter 21 – Household Finance: An Emerging Field, In: George M. Constantinides, Milton Harris and Rene M. Stulz, Editor(s), Handbook of the Economics of Finance, Elsevier, 2013, Volume 2, Part B, Pages 1397-1532, ISSN 1574-0102, ISBN 9780444594068,

    “Overall, the theoretical literature emphasizes that negative equity positions do not automatically trigger default. Other monetary and non-monetary costs, such as relocation and social stigma, may play an important role implying that default may not occur unless equity becomes substantially negative.69 In addition to the option value to delay, default varies in the cross section of households along several dimensions such as mortgage type, leverage ratio, income to loan ratio and income risk.”
    followed by their summation of evidence
    ” Consistently with the models sketched in the previous section, various monetary and non-monetary costs seem to play an important role. Elul et al. (2010) find that, for a given home equity position, default is more likely for households short of liquidity. Guiso, Sapienza, and Zingales (in press) find that default is significantly lower among borrowers that are less likely to become unemployed and have longer tenure—a measure of the attachment to the current location. They are also able to study the moral and social determinants of the attitudes towards strategic default. 82% of respondents believe that it is morally wrong to engage in strategic default, despite the fact that, at least in non-recourse states, insolvency carries no legal consequence.71 Everything else equal, households who think that it is immoral to default strategically are 9.9 percentage points less likely to declare strategic default. In addition, as suggested by the literature on personal bankruptcy (Fay et al., 2002 and Gross and Souleles, 2002a), the decision to default strategically might be driven by other emotional considerations (White, 2010). It has been argued that individuals are more likely to inflict a loss on others when they have suffered a loss themselves, especially if they consider their loss to be unfair (e.g. Fowler, Johnson, and Smirnov, 2004). Indeed, Guiso, Sapienza, and Zingales (in press) find that individuals who feel anger for the economic situation during the Great Recession are more willing to express their willingness to default. Similarly, households who trust banks less, or who know somebody that defaulted strategically, are more likely to declare their intention to do so. This negative externality may be an important amplification mechanism that parallels the effect studied by Campbell, Giglio, and Pathak (2011), who argue that foreclosures impact negatively the prices of nearby houses, presumably because of induced vandalism or neighborhood deterioration”

  97. I note that is Prof L’s last post, I was wondering about his day job.

    Unusually, though he is difficult to follow at times, I seem to be somewhat aligned to him on this. He, like me but unlike others, appears to accept that NE is a causal factor in D but feels the jury is out as to whether that proves SD.

    The US seems quite a different culture esp in non-recourse States. There it appears SDers come out openly and tell their bank they can stuff their mortgage, so called jingle mail. Here SDers do not come out. They disguise themselves as wholesome Ders.

    The term “strategic” is a characterisation of the motivation for the default and different observers will have different criteria for making that characterisation. Personally, I do not classify a default as strategic unless the borrower can clearly afford to pay, e.g. where his circumstances have not deteriorated, but decides deliberately not to do so. GC seems to be less “sympathetic” and characterises anybody who would have made more effort not to default if it were not for the NE as a SDer.

  98. @Brian Woods II – BL is an incredible whirlwind of activity that puts the rest of us academics to shame. I have an excuse since I recently turned 60 but good luck to my younger colleagues trying to keep up with his work output!

  99. bit euro work on this topic regarding ‘motivation’
    cheat sheet and the paper…..
    “We find that solvent borrowers are more likely to default
    strategically when stricter disclosure creates common knowledge about bank weakness. Borrowers are also less likely to repay in the presence of higher uncertainty regarding other borrowers’ financial health, regardless of disclosure rules”

  100. @ GC

    Quality rather than quantity, my mother always told me. I cannot really comment on the quality of Prof L’s output but it often does seem rather cryptic to me – maybe that’s a sign of quality.

    BTW I turned 60 2 years ago so I know the feeling, glad to see I can still do a few sums.

  101. @John Gallagher — The theory section of the Trautman and Vlahu paper is very interesting and very relevant to the Irish case; thanks for the link. I do not put much faith in their experimental data, but that only affects the last part of the paper. The theory section is thought-provoking — has Ireland experienced a borrower run? Given that mortgage holders realized that the banks had very weak and ineffective deterrents and with LTVs very high, does the Trautman-Vlahu theoretical analysis help explain the Irish mortgage arrears explosion?

  102. @Liam Delaney — I ran probit using everything sensible in the database (there are lots of other items in the database but they look useless to me). Income growth is ((net income at application/current net income)-1) and log income is the natural log of current net income. The probit includes dummy interaction terms for every coefficient, where the dummy is 1 for for non-principal private residence loans. About half the sample is PPR and the other half is non-ppr. I hope the output below is readable, and thanks for the suggestions.

    As you suggested, I included Log income and it seems to be a useful addition to the model. Both categories are affected by log income but non-ppr loan defaults are more sensitive to log income than ppr loans (the last estimated coefficient is this interaction term). Income growth has no significant effect on default.

    DDV(dist=probit) default
    # constant nonppr appnets appltv nets ltv incomegrowth logincome nonpprappnets nonpprappltv nonpprnets nonpprltv nonpprincomegrowth nonpprlogincome

    Binary Probit – Estimation by Newton-Raphson
    Convergence in 5 Iterations. Final criterion was 0.0000032 <= 0.0000100
    Dependent Variable DEFAULT
    Usable Observations 31396
    Degrees of Freedom 31382
    Skipped/Missing (from 37124) 5728
    Log Likelihood -20193.6865
    Average Likelihood 0.5256115
    Pseudo-R^2 0.0817386
    Log Likelihood(Base) -21491.4679
    LR Test of Coefficients(13) 2595.5628
    Significance Level of LR 0.0000000

    Variable Coeff Std Error T-Stat Signif
    1. Constant 0.812460477 0.214795888 3.78248 0.00015528
    2. NONPPR 2.350584453 0.282668744 8.31569 0.00000000
    3. APPNETS -0.254790348 0.079885616 -3.18944 0.00142549
    4. APPLTV -0.847334044 0.057481318 -14.74103 0.00000000
    5. NETS 0.398108189 0.022812875 17.45103 0.00000000
    6. LTV 0.717967525 0.024770448 28.98484 0.00000000
    7. INCOMEGROWTH 0.000035424 0.000068516 0.51702 0.60513919
    8. LOGINCOME -0.125072930 0.020641073 -6.05942 0.00000000
    9. NONPPRAPPNETS 0.179627098 0.080224598 2.23905 0.02515249
    10. NONPPRAPPLTV 0.820364257 0.065764595 12.47425 0.00000000
    11. NONPPRNETS -0.000065624 0.000051698 -1.26937 0.20430811
    12. NONPPRLTV -0.161168576 0.020694709 -7.78791 0.00000000
    13. NONPPRINCOMEGROW -0.000035435 0.000068516 -0.51718 0.60503009
    14. NONPPRLOGINCOME -0.276780222 0.027428926 -10.09081 0.00000000

  103. @ GC

    That’s a bit of a sore brainer for someone with an inadequate Wiki education on these matters. Trying to get my head around the NONPPR aspect. Am I correct in this interpretation: let’s say I am modelling NONPPRLTV of 1. Do I have a contribution to sigma of .718 due to LTV and -0.161 due to NONPPRLTV i.e. a net contribution to sigma of .557?

  104. @GC
    Thought you may enjoy it,in fairness i did not get too bogged down in the math,at this stage off my career more a big picture guy !
    But i do have a few years on you ‘old’ guys:)
    Terrific teaser,if you get a chance please post the full paper and best off luck at the conference.
    Reading the objections here in NY/Delaware for Fridays IRBC BK hearing-yikes !
    Its a long way from over just yet,once again have all the court filings not sure if any domestic interest shur its only a BILLION off assets involved….

  105. @ GC

    My read of some of this probit stuff is as follows:

    Your original 5 parameter probit predicts accurately whether a person would default or not on (geometric) average 52.1% of the times

    The enhanced 14 para probit increases this average to 52.6%

    A crude model which says everyone has the same 40% chance of defaut would be right on average 51% of times.

    It’s not clear to me that the probit model significantly increases the predictive power of default for this sample.

  106. More study on this probit thing. Examples on the Internet show probit capable of predicting outcomes on 85% of occasions. GC’s analysis indicates that probit increases predictability from 51% to 52%. This to me shows that the underlying linear model doesn’t fit. Better to revert to Figure 1 which is a straightforward continuous histogram evidence of a correlation between Default and LTV. Invoking probit smacks of intellectual bullyism and is not justified.

    I will make these points at Dew. I will be the guy with the false beard and a turban. I may be unlucky enough to be sitting beside Prof L who will attack me with a giant cucumber. Make sure you catch the action on YouTube.

  107. @Gregory

    A few things:

    Your results are obviously more credible having included these controls.

    Minor point but interaction terms in probits are tricky. Would be good, as sense check, to run a linear probability model (LPM)

    STATA’s “dprobit” command gives simple marginal effects at the mean of the independent variables.

    Your model controls for income. I think the tenor of a lot of the comments here is whether, even with this, that LTV is showing strategic default in the abscence of information about outgoings including other types of debt the people are servicing, dependent children and so on. I can hear your point that these complicate the model and also the argument they should be uncorrelated with LTV. But you must concede that you are effectively saying that the LTV variable is not picking up any unobserved heterogeneity in ability to pay. None of the comments above have really got under the skin of that point other than to dismiss it. Brian Woods II point that we should just use correlations instead of a correctly controlled statistical model is wrong and will lead to potentially overestimating the extent of strategic default.

    There is a lot of research to show that one thing that drives behaviour is perception that you are in line with social norms. A result that widely travels claiming large amounts of strategic default could itself contribute to higher degrees of strategic default. Even if we accept a causal coefficient on LTV, the pseudo R-squared is small indicating a vast amount of heterogeneity that is basically the many social, cultural and unobserved financial determinants of default.

    Anyway, this has been an interesting post possibly near an end!

  108. @ LD, GC

    I can see that average likelihood is not a good measure of goodness of fit. The model could be entirely accurate and we would still get average likelihoods in the 50% vicinity. The examples I saw on on the web are where the 0/1 variable swings from being very unlikley to being very likely, so that a model can aspire to actually have predictive powers. Where the chances of 1 vary in a middle range the model has no hope of having predictive power but it might give a good fit to probabilities.

    But the pseudo R^2 does purport to be a measure of good fit and at .08 surely that is unconvincing.

    @ LD are you implying that publishing these results is somehow irresponsible in that it may give others bad thoughts? If so, is that because you are unconvinced of the validity of the conclusion or would you be critical of its publication even if the conclusion was irrefutable? Either case I think that a bit unfair.

  109. @JG, As you say,”Shure it’s only a billion”….. But the Special Liquidator’s US “smash and grab” raid has gone seriously awry! Even sidelined Linklaters for the world’s biggest lawyers in Skadden – Linklaters must have been making a total *&^$!! of it to date. There will be a galaxy of lawyers (That’s what they call a big group of them believe it or not) collecting in Delaware on Friday afternoon. See you in Court 6 in Wilmington tomorrow, John?

  110. @WSTT,are you buying after……yep just waiting for confirmation it’s a go,should hear by lunchtime today.Let you know over at the other tread,it’s a very flattering almost fawning profile of the minister,he’s all solem and serene almost religious !
    It’s the Business Week article.
    Gregory here does terrific work on mortgages,don’t want to ruin his tread,catch up at Financial Diplomacy,linked John’s brief hope you don’t mind 🙂

    @Liam Delaney,the numbers in default on BTL are not supported by the growth in rental rates,declining vacancy factors.The variables are many and varied,contagion is definitely an issue.
    For the default rates to reflect the true state off play in BTL,you would have downward pressure on rental rates not upwards,increasing vacancy levels not decreasing,overhang off inventory it ain’t so….cause they strategically defaulting.

  111. @Liam Delaney — Thanks for the comments. I spent the day getting rid of the interaction terms and instead estimating separately on all loans, ppr loans, buy-to-let, and multiple property loan accounts. I also fixed an issue with the bandwidth, did some more thorough data cleaning, etc. as will be discussed in the paper eventually, I promise. No marginal probability effects; that is a nuisance but I will cook up the code shortly.

    I agree with BW II above that it is on balance a bad idea to leave this evidence secret for social-political reasons, but I understand the logic. On balance I think openness is better in this case.

    Thanks for the useful comments. If anyone is interested I will leave it for public display.

  112. @ GC

    Thanks for that data. I myself have been doing a bit more investigation of the significance of Pseudo R^2. The following is a simulation in that regard.

    The inputs to this simulation (1000 model points) is the range of the independent variable X (which is assumed uniformly distributed) and the median value of the probability of the (0/1) dependent variable Y being 1. Then using the calculated constant the probit model is used to establish the Pr(Y=1) for each model point. Y is then simulated and from these values I calculate the Pseudo R^2. It turns out to be very low, pseudo indeed and points to a .08 being significant. The reason is of course fairly obvious. Because Y is a 0/1 binary there will always be a significant squared difference between the actual outcome and its modelled probability even if the latter is precise as it is of course in the simulation.

  113. Beta is also an input – a Table showing the dependence of Pseudo R^2 on Beta and Median Pr(Y=1) is the output.

  114. @Brian Woods II – sorry if it was unclear but I would never argue that valid results should be suppressed for a reason like that. My point is that there are still good reasons to think that the LTV coefficient is an overestimate of the extent of strategic default and, as you have noticed yourself, the model fit shows that vast amounts of default behaviour (even among this very selected sample who have already submitted an SFS) are explained by other factors. So please interpret my remark there as saying the paper should be communicated with appropriate caveats.

  115. @Gregory just to repeat the point made to Brian. I would never argue to suppress valid results. The question I would ask though in highly volatile situations where a result might cause a feedback effect is at what stage do you feel confident enough in a set of results to put forward a claim that could influence the situation. I think this has been a useful post and hopefully in the spirit of testing a result in a seminar before being willing to claim that it is true or at least not obviously explained by things a reasonable reviewer could point to. I have also hoped there would be more interactions like this on the blog even if they might be very boring for some of the readers.

  116. @GC
    Thanks for the tables and figures.

    I find Figure 3 is very interesting w.r.t. strategic defaults. The data is quite worrying. I don’t think I’ve seen such data displaying how bad the situation is.

    In Fig. 3, there does seem to be a different slope for the high LTV vs the low LTV, which would imply there is some interaction between LTV and Payment to Income ratios.

    I can’t believe that the arrears rate stabilises at below 100% at Payment to Income ratios, PtI, of >1. This would require a transfer from their savings (or family) to the morgage for those people to not be in arrears.

    Table 1 is very worrying. I don’t think I’ve seen figures which are better at showing the problem we face in Ireland. The median PtI is .45! With it that high, I’m just surprised the arrears rate isn’t higher. And this is in PTSB, which has a high portion of tracker morgages, which would lead to lower PtIs than if they were on variable rate morgages.

  117. Keep in mind that the sample is mortgages with an SFS which is a small, troubled subset of all mortgages. But I agree that this subset of troubled mortgages is certainly a collection of troubled mortgages! The median PTI is very high in this selected subset.

  118. @ GC

    Looking at the graphs more closely I think the title for chart 2b should be PPR loans but maybe not

  119. @Brian Woods II — Thanks, that typo is now fixed, and I also added the marginal effects (marginal change in probability of default/marginal change in independent variable), which are reasonably large.

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