Mortgage Choice as a Natural Field Experiment on Choice UnderRisk∗

Philomena M. BaconDepartment of Economics

Lancaster University Management School

United Kingdom

LA1 4YX

Peter G. MoffattSchool of Economics

University of East Anglia

Norwich

NR4 7TJ

United Kingdom

February 18, 2011

∗The authors are grateful to Dan Houser, Glenn Harrison, and other participants at the CEAR Workshop (Econometrics of Choice Under Riskand Over Time) in Denver in January 2011, for useful comments. The first author gratefully acknowledges sponsorship from the ESRC understudentship PTA-031-2004-00221. Data obtained from the UKDA at Essex University. The standard disclaimer applies. Corresponding author:Peter Moffatt, email: p.moffatt@uea.ac.uk

1

MORTGAGE CHOICE AS A NATURAL FIELD EXPERIMENT ON CHOICE

UNDER RISK

Abstract

Microdata from the UK Survey of Mortgage Lenders is used to model borrowers’choices between variable and fixed rate mortgages. The data is treated as a large-scale“natural experiment” on risky choice, with the choice of a fixed rate corresponding tothe “safe choice” in a more conventional experimental setting. The choice is assumedto depend on three factors: risk attitude; expectations of future movements in inter-est rates; and the discount rate. Approximately 280,000 choices, made by borrowersbetween 1992 and 2001, appear in the sample. The ordered probit model is used forestimation, while taking account of a number of econometric issues including miss-ing counterfactuals, selectivity, and endogeneity. Explanatory variables are dividedinto three groups: mortgage price variables; interest rate expectations; and borrowercharacteristics. A number of strong effects are found, including: fixing is more likelywhen interest rates are expected to rise, and the sensitivity to interest rate expectationsappears to rise with the income of the borrower; a larger amount borrowed (i.e. higherpay-offs in the choice problem) increases the propensity to fix; additional borrowersin the borrowing agreement (especially if female) increase the propensity to fix; high-income borrowers are less likely to fix, particularly so if income is“self-certified”. Theresults offer fresh insights into the analysis of risky choice, particularly with regard tothe roles of pay-offs and subjects’ income.

Keywords and phrases: Risky choice; Fixed and variable rate mortgages; counterfac-tuals; interest rate expectations; discounting; ordered probit.

JEL: G20, M13.

2

1 INTRODUCTION

1 Introduction

The decision to purchase a home is undoubtedly one of the most important fi-nancial decisions made in the course of an economic agent’s lifetime. A closelyrelated decision is on how the purchase will be financed. For the majority ofhomebuyers, the purchase necessitates the taking out of a mortgage, that coverssome or all of the purchase price of the property. A variety of types of mortgageare available. The feature of interest in this paper is whether the mortgage in-terest payments are fixed or variable. Borrowers may choose a “variable rate”mortgage, in which case their monthly interest payments would be determinedby the prevailing market rate of interest, which can rise or fall at any time. Alter-natively, they may choose a “fixed rate” mortgage, by which they are contractedto pay a fixed monthly amount over a specified period.

It is clear that the choice between a fixed rate and a variable rate mortgage is aclassic risky choice problem in the economic sense, and the decision resembles,in some ways at least, the type of risky choice problem typically created in labo-ratory settings. The fixed rate is the “safe choice” since it results in a sequence ofmonthly payments that are known with certainty in advance. The variable rate isthe “risky choice”, since it results in uncertainty over future monthly payments1.The choice that is made clearly depends on the risk attitude of the borrower.However, there are two other important determinants of the choice: the bor-rower’s expectations of future movements of interest rates; and the borrower’sdiscount rate, which clearly determines how much importance they attach to theirinterest rate expectations. It is easy to see that alternative combinations of riskpreferences and expectations can produce the same choice: a risk averse bor-rower who expects no change in interest rates might be expected to choose thefixed rate; however, a risk-seeking borrower might also be expected to choosethe fixed rate if they happen to expect interest rates to rise sufficiently steeplyin the near future. Note further that this risk-seeking borrower may alternativelychoose the variable rate, in spite of their expectations of higher interest rates,

1Of course, there is the possibility that making the “wrong” choice can have more serious consequences than simply higher monthly payments.Imagine, for example, a borrower who takes out a variable rate mortgage, and then experiences an unexpected steep rise in the interest rate, tothe extent that they become unable to service the mortgage. Such a borrower is likely to lose their home.

3

1 INTRODUCTION

if their discount rate is sufficiently high, since a high discount rate reduces theperceived importance of higher future payments. The issued raised here are sim-ilar to those addressed by Savage (1971) and Manski (2004), who consideredthe problem of identification in such situations. As prescribed by Manski, weneed to make an identifying assumption about agents’ expectations of futuremovements of interest rates. The identifying assumption adopted here is that,at any point in time, all agents have the same interest-rate expectations, corre-sponding to “market expectations” implied by the prevailing term structure ofinterest rates. Furthermore, by interacting our chosen term structure variablewith borrower characteristics, we will allow the perceived importance of interestrate expectations (which is closely related to the discount rate) to vary betweenborrowers.

The choice data is obtained from the UK Council of Mortgage Lenders (CML).It contains information on a five percent random sample of mortgage contractsfinanced by its members each month between 1992 and 2001. After filtering in-complete data, this amounts to approximately 280,000 observations. The datasetcontains detailed demographics on the borrower as well as information about theloan.

Our principal reason for labelling the study as a “natural field experiment” isstraightforward: this is a situation in which individuals are, in a natural envi-ronment, undertaking a task that bears close similarities to tasks that have beenengineered in laboratory settings by many different researchers over the past fewdecades, with the same central objective of analysing behaviour under risk2. Thestudy also meets many of Harrison and List’s (2004) other criteria for such acategorisation. First, subjects are completely unaware that they are participatingin an experiment. Second, the subject pool consists entirely of ordinary individ-uals, who have self-selected only to the extent that they are purchasing a widelydemanded commodity – a mortgage. Third, the commodity is real and purchasedunder normal economic conditions, in a highly competitive market. Fourth, in-formation regarding choices is freely available to all subjects, and the choice

2Some key examples of laboratory studies of choices between lotteries are: Kahneman and Tversky (1979); Hey and Orme (1994); Loomesand Sugden (1997).

4

1 INTRODUCTION

itself is at the complete discretion of the subject, who is normally unhindered bytime constraints. Fifth, the task, to choose between a fixed and a variable rate,requires no former experience, although some subjects are not first-time buyers,and so have presumably made a similar decision at least once previously.

One of the major attractions of this natural experiment is the salience of theincentives. Completion of the choice task results in a binding contract with re-sulting pay-offs projected months or years into the future. Such incentives arehigh: the choice made can result in quite substantial gains or losses relative to therejected alternative. In Section 2, we present examples of the types of outcomesactually arising in the context of the dataset. Given the salience of the outcomeand the unlimited decision time, there is little doubt that subjects in this naturalexperiment can be relied upon to invest whatever cognitive effort is required tobe in a position to express their true preferences. Also, the task is performedonce and only once, thereby avoiding the type of between-task contamination(see, for example, Holt (1986)) that may arise when a sequence of tasks is per-formed, as is routine in laboratory settings.

Another class of natural experiment with salient incentives is that of the GameShow. This research area has enjoyed a flurry of interest in recent years (see,for example, Post et al., 2008). Choices analysed in this setting are clearly forreal and have high stakes. However, researchers in this area have faced a raftof criticism: the participants self-select in a rather extreme way, making it hardto justify the use of results in predicting the behaviour of the wider population;only a very short period (usually a few minutes) is available for each delibera-tion; the decision-maker is operating in an unnatural and unfamiliar setting, andtheir decision is likely to be influenced by the presence and behaviour of thestudio audience. Clearly, all of these problems are categorically avoided in thenatural experiment considered in this paper.

Our natural experiment has further advantages over other types of experiment,that we set out to exploit to the full. One concerns the role of subject income.Economists are very interested in the effect of individual income on risk attitude.However, it is widely accepted that, in the context of laboratory experiments,

5

1 INTRODUCTION

“outside” income (or “permanent” income) has only an indirect effect on be-haviour. The usual measure of “income” in these settings is simply the incomeearned in the experiment, and the utility function is defined over this variable. Incontrast, in the context of our natural experiment, the pay-offs take the form ofmonthly payments that will come directly out of the subject’s monthly income.Hence, what is normally considered to be “outside” income may be naturallyexpected to have a direct effect on behaviour. We are keen to exploit this oppor-tunity to quantify the effect of income on risk attitude.

One final advantage is the huge sample size: the choices of 280,654 decision-makers are used to estimate the various models we construct. This is an orderof magnitude higher than the sample sizes typically encountered in lab-basedresearch, and, accordingly, has the potential to lead to considerably strongerconclusions regarding some of the effects in which behavioural economists maybe most interested.

Of course, the fact that this analysis is based on a natural field experiment, withfeatures that set it far apart from the “sterility” of the laboratory environment,presents us with a number of interesting and challenging econometric issueswhich add further potential for this work to contribute to the body of research inthis field. The first of these is the absence of data on the counterfactual choice.While the rate struck by each borrower, whether they chose fixed or variable, isobserved, the rate that they would have obtained had they made the other choice,is unknown. This requires some method of imputation, of which, as we shallsee, there are a number of possibilities. The second econometric issue is thatof selection bias: since borrowers have engaged in a process of search for thepackage that they find most attractive, it is likely that the choice they have madewas driven by the unusually attractive features of the chosen deal, for exam-ple, having a lower rate than expected. If the rates struck are to be analysed,as they need to be in the process of imputing the counterfactual rates, such se-lection bias must be addressed. The third issue is endogeneity. In consideringborrowers’ choice between different rates, we need to examine how these rateshave been determined. They are clearly set by the lenders, and, importantly, thelenders are using some of the same criteria in setting rates, namely those relating

6

1 INTRODUCTION

to interest rate expectations, as borrowers use in choosing between them. Hencethe endogeneity of rates offered to borrowers must also be addressed in the esti-mation process, in order to obtain consistent estimates of the demand parameters.

Work has previously been carried out on the borrower’s decision to fix rates. Almand Follain (1984) and Campbell and Cocco (2003) provide theoretical treat-ments; the latter, like us, extract a measure of interest rate expectations from theterm structure of interest rates. Empirical work on the fixing decision has typi-cally consisted of binary choice models applied to relatively small sample sizes.For example, Dhillon et al.(1987) considered the choices of 78 households inLouisiana, USA; Brueckner and Follain (1988, 1989) used a dataset consistingof 475 households from across the USA; Leece (2000) used a sample of 762 UKhouseholds; Coulibaly and Li (2009) consider the choices of 2,878 householdsacross the USA. The key determinant of the choice found in most of this litera-ture is the rate differential, that is, the variable denoted in our section 3 as pf −pv.Some researchers have gone further by considering more than two categories ofthe fixing decision. Sa-Aadu and Sirmans (1995) conside five different levels offixing, and use a multinomial logit model to condiser the choice between thesealternatives of 345 midwestern (USA) households. The multinomial logit modelis also used by Phillips and Vanderhoff (1994) who consider the choice betweenthe three alternatives: government-backed fix; ordinary fix; and adjustable rate.Their sample size is 6,894.

There are many examples of risky choice research being taken into“the field”such as Binswanger (1980), who studied the decisions of Indian farmers, Harri-son et al. (2007), who studied a broad cross section of the Danish population,and Harrison et al. (2009), who studied villagers in Uganda, India and Ethiopia.These studies have clearly benefitted in various ways from their “field” settings,not least in being able to offer pay-offs that are “high” relative to local income.However, with the exception of the gameshow studies mentioned earlier, full-scale “natural experiments” which focus exclusively on risky choice decisionsare hard to find in the literature. To our knowledge, Bacon (2009) is the onlyempirical researcher to have treated the mortgage choice problem in the contextof risky choice, thereby contributing to the literature on the estimation of factors

7

2 FIXED AND VARIABLE RATE MORTGAGES IN THE UNITED KINGDOM

determining risk attitudes. The contribution of the current paper is to bring thisresearch area further into the domain of behavioural economics, in particular byseparating the role of risk attitude from that of expectations, in the spirit of Sav-age (1971) and Manski (2004). The ultimate objective of this study is to use thedata to estimate the effects of various borrower characteristics on risk attitude,and to compare the obtained estimates to the results of other experimental andfield studies that have pursued estimates of the same effects.

The paper is set out as follows. Section 2 briefly considers some institutionalissues relating to the choice between fixed and variable rates in the UK, andalso, for the sake of further motivation, provides specific examples of monetaryoutcomes that would have arisen from the different choices at selected points intime. In section 3, we develop a model of the choice between fixed and variablerates, and consider how the model should be estimated in order to deal with thevarious econometric issues raised earlier in this section. In section 4 we exam-ine the data. In section 5 we present and discuss the results. Section 6 concludes.

2 Fixed and Variable Rate Mortgages in the United Kingdom

The uptake of fixed rate mortgages in the UK has been of growing interest topolicy-makers in recent years3. Meen (2002) reports that house prices in theUK are particularly sensitive to changes in short-term interest rates. The result-ing house price volatility has undesirable consequences for the economy as awhole. A switch to a higher proportion of fixed-rate mortgages has the poten-tial to weaken the link between short-term rates and the housing market, andtherefore to bring about stability in the latter. An example of a stable housingmarket combined with a high proportion of fixed rate mortgages is found in theNetherlands, where medium- to long-term fixed rate mortgages have accountedfor around 70% of mortgage financing over the last two decades4.

3See, for example, Miles, (2003) Chapter 34See Miles (2003) Chapter 1

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2 FIXED AND VARIABLE RATE MORTGAGES IN THE UNITED KINGDOM

In 2003, the then UK Chancellor of the Exchequer Gordon Brown advocated awidening in the use of fixed-rate mortgages as a precondition for British entryinto the Euro. At the time of the 2003 Budget, he commissioned Professor DavidMiles to investigate why long-term fixed rate mortgages occupied such a smallshare of total business, and to make recommendations for addressing the issue.The final report appeared as Miles (2004). His recommendations included mea-sures designed to raise levels of borrowers’ understanding of interest rate risk,and measures making it less risky for lenders to lend at long-term fixed rates.

Figure 1 depicts the breakdown of new mortgage business between fixed andvariable rates in the UK over the period 1992 to 2007. Prior to 2005 there ap-peared to be a broad preference for variable rates. However, more recently, per-haps partly as a consequence of changes implemented as a result of the Milesreport, a steady increase in the take-up of fixed-rate deals has taken place. Thistaste change towards the take-up of fixed rate mortgages since 2004 brings theUK mortgage market closer to that of the USA where there is a strong preferencefor fixed rate mortgages.5

A feature of the UK mortgage market is that UK borrowers who choose to fixare typically reluctant to fix for long periods. A two-year fix is fairly typicalin the UK market. This contrasts starkly with the 10-15 year fixes frequentlyseen in Europe, and the 15-25 year fixes seen in the USA. When the period ofthe fix has elapsed, the rate automatically reverts to the Standard Variable Rate(SVR). Harsh early-redemption penalties typically apply if a borrower choosesto opt out of a fixed-rate agreement. In recent years upfront fees have also beenintroduced, some of which are refundable at the end of the fixed rate term, as adeterrent to early redemption.

To complete this section, we bring into focus the size of the pay-offs that char-acterise the choice problems of interest, by illustrating the monetary gains andlosses that arise in particular scenarios. We consider a £100,000 mortgage, and

5The interest rate survey of the USA Federal Housing Finance Board.

9

2 FIXED AND VARIABLE RATE MORTGAGES IN THE UNITED KINGDOM

Figure 1: PROPORTIONS CHOOSING FIXED AND VARIABLE: 1992 - 2007.Source: Survey of Mortgage Lenders. UKDA Essex.

the interest-only monthly payments6 that would have actually been made by bor-rowers over a two-year period, under each interest rate regime, had the deals beenstruck on particular dates. The dates we consider are June 1996, and June 1998.The path of the monthly repayments relating to these deals is shown in Figures2 and 3. For the fixed-rate calculation we use the mean fixed rate struck in thefirst month of the two-year period; for the variable-rate calculation, we use themean variable rate for each month within the two year period. The total amountspayable under each deal (assuming zero discounting) are reported in Table 1.Also shown in Table 1 are the present values of the streams of payments on theassumption of a discount rate equal to the prevailing central bank base rate.

As can be seen in Table 1, for the first period the fixed rate deal was cheaper by£1,468, whilst for the second period the variable rate deal was cheaper by £422.Note also that when the discount rate is assumed to be positive, and equal to

6For simplicity we treat capital as being repaid at the end of the mortgage term, and do not add it to the monthly interest costs.

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2 FIXED AND VARIABLE RATE MORTGAGES IN THE UNITED KINGDOM

Figure 2: PATH OF COMPARABLE MORTGAGE REPAYMENTS: JUNE 1996 – MAY 1998.

Figure 3: PATH OF COMPARABLE MORTGAGE REPAYMENTS: JUNE 1998 – MAY 2000.

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2 FIXED AND VARIABLE RATE MORTGAGES IN THE UNITED KINGDOM

the prevailing base rate of interest, the pay-offs, computed as the difference inpresent values of the two payment streams, are smaller in magnitude than underzero discounting, but still sizeable. The most revealing feature of these two ex-amples is that in both cases, a “myopic” borrower, that is, one who bases theirdecision only on the price differential prevailing at the start of the two-year pe-riod, will make the “wrong” choice. The two graphs make this very clear. InFigure 2, the variable rate starts off below the fixed rate, but is above the fixedrate for most of the 2-year period, resulting in a net loss of £1,468 if the variablerate is chosen. In Figure 3, it is the fixed rate that is lower at the start of theperiod; thereafter, successive falls in the variable rate result in a net loss of £422from choosing the fixed rate.

Table 1: SUMMARY OF INTEREST PAYABLE UNDER DIFFERENT RATE REGIMESVariable Rate Fixed Rate

2 Years Discount Rate Present Value Present Value Present ValueFrom Assumed Rate of payments Rate of payments of Pay-off

Jun 1996 0% 5.53% £13,303.15 5.92% £11,834.98 ±£1,468Jun 1996 6.00% 5.53% £12,464.35 5.92% £11,124.59 ±£1,340Jun 1998 0% 7.64% £12,801.21 6.61% £13,222.95 ±£422Jun 1998 7.25% 7.64% £11,908.28 6.61% £12,271.85 ±£364Notes:1. The two discount rates assumed for each period are zero, and the prevailing central bank base rate.2. The interest rates shown in the table are average rates in the first month of the two-year period.

In the models developed in Section 3, we assume that borrowers are not myopic;they are forward-looking, basing their expectations of interest rates on the mar-ket expectations that are embodied in the current term structure of interest rates.It is therefore interesting to investigate what these expectations are in the contextof our two examples. Referring ahead to figure 8, which shows the time pathof the 3-month yield and the 10-year yield, we see that the yield spread in June1996 was +2.52 percentage points, whilst in June 1998 it was -1.71 percentagepoints. Hence we infer that, in June 1996, the market expected a fairly steeprise in interest rates, while in June 1998, the market expected a fairly steep fall.By incorporating these expectations into the decision-making process, forward-looking borrowers are guided towards the choice of a fixed rate in June 1996, andtowards a variable rate in June 1998. Hence, in both cases, the prevailing interest

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3 THE MODEL

rate expectations are seen to guide borrowers towards the choice that eventuallyturns out to be “correct”.

3 The Model

Since this paper is concerned with the choice between fixed and variable ratemortgages, and not the overall demand for mortgages, we commence from theassumption that total demand is fixed. If it aids understanding, the market can beperceived as consisting of a single borrower who has already made the decisionto take out a mortgage, and is in the process of deciding between a fixed rate anda variable rate. In this context, the demand function discussed below may simplybe interpreted as that single individual’s propensity to choose a fixed rate over avariable rate. This propensity to fix will be denoted as y∗.

Figure 4 presents a demand and supply diagram for fixed and variable rate mort-gages. Total demand (y∗max) is represented by the vertical line. On the verticalaxis is measured the fixed-variable price differential (i.e. the difference in therates): pf − pv. The focus of the analysis is the proportion of total demand thatis fixed-rate. This is represented by the downward sloping curve, which conveysthe fact that a rise in the interest rate at which the fixed-rate deal is struck, ceterisparibus, causes a fall in the propensity of a typical borrower to opt for the fixedrate. Supply of fixed rate mortgages is represented by the horizontal line. Thisis because we are assuming that the lender chooses both the fixed and variablerates, which gives rise to a horizontal supply curve at (pf − pv)1. The resultingquantity demanded of fixed rate deals is then given by y∗1 , and the remainder ofdeals demanded y∗max − y∗1 are variable-rate.

Clearly, if lenders increase the price of the fixed rate and hold the variable rateconstant, the quantity demanded (y∗1) is expected to fall. The slope of the de-mand curve is therefore related to the inverse of the negative coefficient on thevariable representing pf − pv, in the demand equation estimated later. However,a crucial point is that the factors that influence lenders’ choice of fixed rate are

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3 THE MODEL

Figure 4: THE MARKET FOR FIXED RATE (AND VARIABLE RATE) MORTGAGES.

some of the same factors that determine the demand for fixed rate deals. Thefactors in question relate to interest rate expectations. If the market expects in-terest rates to rise, borrowers’ propensity to choose fixed rates are likely to risein anticipation of their expectations being fulfilled. However, simultaneouslylenders are likely to raise the price of their fixed rate deals. In Figure 4, twothings happen in response to the expected increase in interest rates. The entiredemand curve shifts to the right; and the horizontal “supply curve” rises. Theoverall effect on the number of fixed deals is ambiguous, and depends on therelative magnitudes of these two effects. In order to separate out the effects, anInstrumental Variables (IV) estimator is required.

This leads to the important question of how interest rate expectations are mea-sured. Here we appeal to expectations theory (Sargent, 1972), according towhich market expectations of future movements of interest rates may be inferredfrom the slope of the yield curve: the steeper the yield curve, the more steeplythe market expects interest rates to rise. Of course, an assumption that is requiredin order to make this claim is that the term premium is invariant over time, sothat all changes in the slope of the yield curve can be attributed to changing mar-ket expectations of interest rates. We represent the slope of the yield curve by

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3 THE MODEL

the difference between the yield on a long-dated bond and a short-dated bond.For the former, we use the 10-year zero-coupon bond yield, and for the latter,the 3-month zero-coupon yield. We refer to this difference as the yield spread,and denote it as s. By including this variable in the demand equation, we are as-suming that all borrowers have interest rate expectations that correspond to thecurrent value of the yield spread. This is the identifying assumption, required inthe spirit of Manski (2004), that enables us to separate out the effect of interestrate expectations from that of preferences.

We can go further than this. It is natural to expect the discount rate to varybetween borrowers, which implies that some borrowers will attach more impor-tance than others to market expectations of interest rate changes. We will allowfor this by interacting the yield spread variable with borrower characteristics thatare thought to determine the discount rate. By virtue of the inclusion of both sand its interactions with borrower characteristics, as determinants of the fixingpropensity, we claim to be controlling for both interest rate expectations and dis-counting, so that the effects of all other explanatory variables may interpreted interms of risk preferences.

Characteristics of the borrower that that determine the demand for fixed rateswill be assumed to determine the position of the demand curve in Figure 4. Forexample, if age of borrower has a negative effect on the propensity to fix, then anincrease in age brings about a leftward shift in the entire demand schedule. Age,as well as a number of other characteristics, do indeed turn out to have importanteffects.

The variable y∗ has been introduced as the propensity to fix, and this variablewill appear on the left hand side of all specifications. However, a feature of theavailable data is that the exact length of fix is unobserved. We instead observeone of three outcomes: no fix; fixed for up to one year; fixed for a period greaterthan one year. In view of the ordinal nature of this dependent variable, we shallestimate all models in the framework of the ordered probit model.

All specifications have the following structure:

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3 THE MODEL

y∗ = α1s + α2′(s ∗ z) + α3 (pf − pv) + α4 (pv − r) + α5r + β

′x + u (1)

where:y∗ is the propensity to fix;s is the 10-year less 3-month yield spread;z is a vector of borrower charateristics assumed to influence the discount

rate;pf − pv is the fixed-variable price differential;pv − r is the variable-rate premium;r is the central bank base interest rate;x is a vector of borrower characteristics assumed to influence risk atti-

tude;u is the error term.

The differences between the various specifications are in the manner in whichthe variables pf and pv, and their counterfactuals, are defined. The most obvi-ous way in which to impute the counterfactual prices is to follow Phillips andVanderhoff (1994) by simply using the mean of the prices applying to all of theactual data for a given month. That is: for fixed-rate borrowers, the variableprice is assumed to be the mean rate struck by all variable-rate borrowers in thesame month; for the variable rate borrowers, the fixed price is assumed to be themean rate struck by all the fixed-rate borrowers in the same month. The meansso obtained are used to construct the price differential p̄f − p̄v, as well as thevariable-rate premium p̄v − r. Note that this notation, with a single bar over eachprice variable, indicates that the means are used only to replace the counterfac-tual prices; actual price data is still used for the chosen alternative.

A superior method for imputing counterfactual prices is to follow Brueckner andFollain (1989) by using predictions from an OLS regression of prices (for thosewho made the relevant choice) on a set of explanatory variables. The price equa-tions estimated take the following form:

pf = γ1,f r + γ2s + γ3s2+ γ4s

3+ δf

′w + vf (2)

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3 THE MODEL

pv = γ1,v r + δv′w + vv (3)

where:pf is the fixed price (interest rate of the fixed rate mortgage);pv is the variable price (interest rate of the variable rate mortgage);r is the Bank of England Base rate;s is the yield spread;w is a vector of borrower characteristics that determine the rate offered;vf and vv are error terms.

Note that the fixed rate pf is assumed to depend (non-linearly) on the yield spreadwhilst the variable rate pv does not. This is because, while it is logical to assumethat lenders set their fixed rates on the basis of expectations of future movementsin interest rates, variable rates traditionally shadow the BoE base rate and are nottherefore based on such expectations.

When (2) and (3) are estimated by OLS, and the resulting predictions used toimpute counterfactual prices, the price differential and variable-price premiumare denoted respectively by p̂f − p̂v and p̂v − r. Note that, as previously with theuse of “bars”, a single “hat” in these expressions indicates that only the counter-factual values have been replaced by OLS predictions; actual data is used whereavailable.

Yet another possible method for imputation, used previously by Brueckner andFollain (1988), is one that allows for selectivity. As previously remarked, a pricethat is observed is for a deal that has been chosen, and the deal was chosen be-cause of its attractiveness in terms of features including price. Given this, it islikely that the two methods of imputation described above will result in imputedprices that are, on average, biased downwards. To correct for this “selectionbias”, Heckman’s (1979) two-step method is used to estimate (2) and (3). Whenestimates thus obtained are used to generate predictions, the resulting price dif-ferential and variable-price premium will be denoted respectively by p̃f − p̃v andp̃v − r.

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3 THE MODEL

Table 2: SUMMARY OF MODEL FEATURES AND NOTATION

Model pf − pv pv − r Counterfactual Selection bias Endogeneity1 p̄f − p̄v p̄v − r ✓

2 ¯̄pf − ¯̄pv ¯̄pv − r ✓ ✓

3 p̂f − p̂v p̂v − r ✓

4 ˆ̂pf − ˆ̂pv ˆ̂pv − r ✓ ✓

5 p̃f − p̃v p̃v − r ✓ ✓

6 ˜̃pf − ˜̃pv ˜̃pv − r ✓ ✓ ✓

Key to notation Description⋅̄ Sample means replace missing values only¯̄⋅ Sample means replace all values⋅̂ OLS prediction replaces missing values onlyˆ̂⋅ OLS prediction all values⋅̃ Heckman prediction replaces missing only˜̃⋅ Heckman prediction replaces all values

One further econometric problem that needs to be addressed is the endogeneityof prices. Because lenders, in the process of setting interest rates, take accountof the same factors (in particular interest rate expectations) as do borrowers inthe process of choosing whether to fix, an assumption of price endogeneity mustbe incorporated in order to isolate the effect of such factors on the demand forfixes. For this purpose, an IV estimator is used. IV estimation of (1) involves re-placing all observations of price, including the observed prices, with predictionsfrom the first-stage estimation procedure. When all observations are replaced bymonthly means, the variables will be denoted by ( ¯̄pf − ¯̄pv) and ( ¯̄pv − r). Whenall observations are replaced by OLS predictions, we will have ( ˆ̂pf − ˆ̂pv) and( ˆ̂pv − r). Finally, when all observations are replaced by predictions from theHeckman selection model, we will have ( ˜̃pf − ˜̃pv) and ( ˜̃pv − r).

Equation (1) will be estimated using six different models, which are summarisedin Table 2. Model 6 is the most preferred on theoretical grounds, since it simul-

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3 THE MODEL

Figure 5: THE ORDERED PROBIT MODEL; DENSITY FUNCTION OF “PROPENSITY TO FIX”, AND ITSRELATIONSHIP TO THE OBSERVED FIXING DECISION

taneously deals with all three of the econometric problems identified: missingcounterfactuals; selection bias; and endogeneity.

Let us finally turn to the dependent variable. As mentioned, this has three pos-sible outcomes: variable; fixed for up to one year; and fixed for over one year.If the variable rate is treated as “no fix”, then it is clearly seen that the threeoutcomes are ordered, and the ordered probit model (McKelvey and Zavoina,1975) is appropriate. The underlying latent continuous variable is “propensityto fix”, denoted as y∗ throughout this section. Figure 5 shows the distribution ofy∗. Note that the mean propensity to fix, β′x say, depends on the explanatoryvariables appearing in the vector x and that actual propensity to fix is distributednormally (with variance normalised to 1) around this mean. The outcome is as-sumed to be determined according to where the propensity to fix falls in relationto two “cut-points” κ1 and κ2. For example, as indicated in Figure 5, a propen-sity to fix between κ1 and κ2 would result in a short fix being chosen. The twocut-points are estimated along with the parameters contained in the vector β, bymaximum likelihood. Note that the vector β does not include an intercept, sinceit would not be separately identifiable from the two cut-points.

Another possible approach is the Interval Regression model (Stewart, 1983).Here, the underlying variable is taken to be the desired length of the fix, mea-

19

3 THE MODEL

Figure 6: THE INTERVAL REGRESSION MODEL; DENSITY FUNCTION OF LENGTH OF FIX, AND ITSRELATIONSHIP TO THE OBSERVED FIXING DECISION

sured in years. This is illustrated in Figure 6. Desired length of fix is assumed tovary between −∞ to +∞, but negative values are censored and correspond to thechoice of a variable rate. If the desired length of fix is positive, we observe theinterval (either (0,1) or (1,+∞)) in which the actual length of fix lies. As withthe ordered probit model, the underlying variable is assumed to have its meandetermined by a set of variables denoted by the vector x, and to be normallydistributed around the mean. However, there are a number of differences fromordered probit. Firstly, the variance parameter is identified and is therefore aparameter that requires estimation. Secondly, the intercept in this model is alsoidentified. Thirdly, the cut-points in this model are known values (0 and 1 in thiscase) and therefore do not require estimation.

A question that inevitably arises is which of these two models is preferred.The answer is that, generally, the interval regression model is preferred on thegrounds that knowledge of the cut-points allows greater efficiency with respectto the estimation of the model’s other parameters. However, in the special casein which there are only three outcomes, the two models contain exactly the samenumber of unknown parameters, and, interestingly, they are identical in termsof the value of their maximised log-likelihoods, and therefore their explanatory

20

4 DATA

power7.

Since the variable of interest here has only three outcomes, we may thereforeconclude that ordered probit and interval regressions are equivalent models inexplaining our data. Hence, for our demand equation we shall estimate onlythe ordered probit model, and, accordingly, draw conclusions in terms of the ef-fects of different factors on the borrower’s propensity to fix. However, it is stillconceptually useful to recognise that an alternative, and effectively equivalent,approach would be to consider the length of the fix as the underlying variable ofinterest, and to proceed by estimating the interval regression model.

4 Data

We use data from the UK “Survey of Mortgage Lenders” 8, a monthly dataset ofapproved mortgages by the building societies that are members of the Council ofMortgage Lenders (CML). The CML represents the association of prime lendersin the UK. This means that rates and loan size are competitive and borrowers arecomfortably creditworthy (i.e. having low risk of default); in contrast, the non-prime lender sector of the mortgage market specialises in higher risk borrowersand charge a premium rate for mortgages. The survey consists of a random fivepercent sample of mortgages sold by each lender in the group each month. Weuse the datasets for 1992 to 2001 giving a total of 438,034 observations; we thenfurther select only those mortgages where full financial details are given leavinga net sample size of 280,654.

Tables A1 and A2 in the Appendix present descriptive statistics for binary ex-planatory variables, and other explanatory variables, respectively from the dataset.

Table 3 shows a tabulation of the dependent variable over the sample. We see7Note that, in the trivial case of two outcomes, the ordered probit and interval regression models both become binary probit, and are therefore

equivalent, as in the three-outcome case. For any number of outcomes greater than three, the two models are not equivalent, and the intervalregression model is preferred.

8This data was obtained from the UK data Archive at Essex University, for the perod 1978-2001. This survey was conducted on behalf of thethen Dept. of Transport Local Government and the Regions (1978-2001).

21

4 DATA

Figure 7: Bank of England Base Rate (r) and Mean Monthly Rates for Fixed (pf ) and Variable (pv) Mortgages1992-2001. Source: Fixed and variable rates from the CML dataset; BoE rate from BoE Statistical InteractiveDatabase website: http://www.bankofengland.co.uk

that the majority of borrowers (62%) chose variable rate mortgages, and that ofthose who fixed, most chose a “long fix”, that is, one lasting longer than one year.

Table 3: Distribution of the Dependent Variable y.Value of y Description Frequency Percentage

1 Variable rate 172,877 62%2 Fixed <1 year 11,514 4%3 Fixed >1 year 96,263 34%

Total 280,654 100%

The explanatory variables are divided into three groups: borrower characteris-tics; mortgage price variables; and interest rate expectations. Borrower charac-teristics include income, the number of male and female applicants to the loan,the age of the main borrower, whether income is self-certified, whether the bor-rower(s) is(are) first-time buyers, the size of the advance, the loan-to-income ra-

22

5 RESULTS

tio, the loan-to-value ratio, and whether the mortgage is of repayment type. Themortgage price variables are obtained from various combinations of the fixedprice, pf , the variable price, pv and the BoE base rate, r. The time paths of themonthly means of these three variables are presented in Figure 7. As expected,the base rate is usually the lowest of the three. Of the other two, pf is usually thehigher, that is, fixed-rate deals are typically more expensive than variable-ratedeals.

As explained in Section 3, the variable used to represent interest rate expecta-tions is the term spread,s. The time paths of the two yields that combine to gives are plotted in Figure 8. The way to use Figure 8 is simply to consider which ofthe two lines is higher. For example, during the period 1994-1996, the long yieldwas considerably higher than the short yield, representing a market expectationof increases in the interest rate. In Figure 7, it is seen that this expectation wascorrect, with the base rate rising intermittently until mid-1998.

5 Results

The six models outlined in Section 3 have all been estimated using the data de-scribed in Section 4. Recall that these six models amount to different approachesto estimating the parameters of equation (1). These estimated parameters are allshown in Table 4. Recall also that some of the models (namely Models 3, 4,5 and 6) require preliminary estimation of the two price equations (2) and (3),using either OLS or Heckman’s 2-step procedure. The estimates from these pre-liminary models are all presented in Table A3 in the Appendix.

As stated in Section 4, Model 6 is preferred on theoretical grounds, since itdeals with all three of the econometric problems that have been addressed: miss-ing counterfactuals; selection bias; and endogeneity. For this reason, we shallmainly be using the results from Model 6 (i.e. the final column of Table 4) ininterpreting the effects of the explanatory variables on the propensity to fix.

23

5 RESULTS

Figure 8: COMPONENTS OF s: THE 3 MONTH BOND YIELD AND 10 YEAR BOND YIELD: 1992 TO 2002.

Focusing first on the price variable, we see that the coefficient of ˜̃pf− ˜̃pv in Model6 has the expected negative sign, and is strongly significant. This is consistentwith the downward-sloping demand curve shown in Figure 4, and simply con-firms that a rise in the price of fixes relative to the price of variable deals bringsabout a fall in the demand for fixes. It is interesting to note in passing that thecorresponding variable in each of Models 1, 3 and 5 has a positive coefficient.This confirms the importance of the IV procedure that addresses the endogene-ity of price; Models 1, 3 and 5 all disregard the problem of endogeneity, andconsequently, through a failure to isolate the demand equation, return a pricecoefficient with the incorrect sign.

Next, we see that the coefficient on the variable rate premium ( ˜̃pv − r) is alsonegative and significant. In interpreting this coefficient, we must imagine thatthe price differential ˜̃pf − ˜̃pv is fixed. The interpretation is therefore that if boththe variable rate and the fixed rate simultaneously rise by the same amount, therewill be a fall in the demand for fixes. Next we see that the coefficient of the base

24

5 RESULTS

rate r is also negative. This indicates that at times when interest rates, generally,are very high, fixed rates are less popular. This is perhaps because, at times wheninterest rates are abnormally high, borrowers have particularly strong expecta-tions that they will fall in the future, making fixed deals appear less attractive.

We see that the coefficient of the yield spread s is negative. However, this is sim-ply a consequence of the presence of the two interaction terms. The significantlypositive coefficient on the interaction between s and log(income) indicates thatall borrowers respond positively (i.e. their propensity to fix rises) to expecta-tions of higher interest rates9, and this effect becomes stronger as income rises.In line with our discussion in Section 3, this may be interpreted in terms ofdiscounting: higher-income borrowers have lower discount rates. This result isconsistent with the results of discounting experiments reported by Harrison et al(2002), and also with results obtained using field data on durable good purchasesby Hausman (1979). The other interaction of s with FTB indicates that being afirst-time buyer also appears to reduce the discount rate.

As explained in Section 3, the coefficients of all variables not involving s or itsinteractions, may be interpreted in terms of their effect on risk attitude. Let usnow consider these effects in turn. The log of advance has a positive and signif-icant effect. The size of the advance may be interpreted as a proxy for the levelof the pay-offs in the risky choice problem, in which case the positive coefficientleads us to conclude that higher pay-offs bring about an increase in risk aversion.This result is consistent with results obtained in laboratory experiments by, forexample by Holt and Laury (2002).

9This can easily be verified given the information that log(income) varies in the sample between a minimum of 7.02 and a maximum of 13.91.

25

5 RESULTS

Table 4: ORDERED PROBIT RESULTS FOR MODELS 1 TO 6

Model 1 Model 2 Model 3 Model 4 Model 5 Model 6p̄v − r 0.133∗∗∗

(0.00341)

p̄f − p̄v 0.0843∗∗∗

(0.00311)

¯̄pv − r 0.0715∗∗∗

(0.00579)

¯̄pf − ¯̄pv -0.665∗∗∗

(0.0114)

p̂v − r 0.144∗∗∗

(0.00375)

p̂f − p̂v 0.0779∗∗∗

(0.00330)

ˆ̂pv − r -0.324∗∗∗

(0.0171)

ˆ̂pf − ˆ̂pv -0.945∗∗∗

(0.0233)

p̃v − r 0.373∗∗∗

(0.00371)

p̃f − p̃v 0.362∗∗∗

(0.00328)

˜̃pv − r -0.257∗∗∗

(0.0161)

˜̃pf − ˜̃pv -0.951∗∗∗

(0.0242)

r -0.0533∗∗∗ -0.0923∗∗∗ -0.0505∗∗∗ -0.195∗∗∗ 0.00797∗∗ -0.195∗∗∗

(0.00253) (0.00281) (0.00257) (0.00501) (0.00260) (0.00506)

s -0.373∗∗∗ -0.449∗∗∗ -0.362∗∗∗ -0.136∗∗∗ -0.359∗∗∗ -0.136∗∗∗

(0.0322) (0.0324) (0.0322) (0.0326) (0.0325) (0.0326)

s * Log income 0.0237∗∗∗ 0.0410∗∗∗ 0.0229∗∗∗ 0.0276∗∗∗ 0.0157∗∗∗ 0.0272∗∗∗

(0.00317) (0.00319) (0.00317) (0.00318) (0.00320) (0.00318)

s * FTB 0.0247∗∗∗ 0.0244∗∗∗ 0.0250∗∗∗ 0.0246∗∗∗ 0.0266∗∗∗ 0.0246∗∗∗

(0.00350) (0.00353) (0.00350) (0.00352) (0.00354) (0.00352)

Cont‘d

26

5 RESULTS

Model 1 Model 2 Model 3 Model 4 Model 5 Model 6

Log advance 0.450∗∗∗ 0.422∗∗∗ 0.471∗∗∗ 0.495∗∗∗ 0.462∗∗∗ 0.507∗∗∗

(0.0172) (0.0173) (0.0172) (0.0175) (0.0174) (0.0174)

Log income -0.284∗∗∗ -0.242∗∗∗ -0.300∗∗∗ -0.350∗∗∗ -0.289∗∗∗ -0.351∗∗∗

(0.0176) (0.0177) (0.0177) (0.0179) (0.0179) (0.0179)

Self cert’d -0.292∗∗∗ -0.283∗∗∗ -0.283∗∗∗ -0.259∗∗∗ -0.307∗∗∗ -0.260∗∗∗

Income (0.00492) (0.00493) (0.00494) (0.00495) (0.00498) (0.00494)

#Males -0.0311∗∗∗ -0.0334∗∗∗ -0.0337∗∗∗ 0.0751∗∗∗ -0.0563∗∗∗ 0.0860∗∗∗

(0.00683) (0.00688) (0.00684) (0.00730) (0.00691) (0.00723)

#Females 0.0415∗∗∗ 0.0386∗∗∗ 0.0373∗∗∗ 0.0998∗∗∗ 0.0133∗ 0.115∗∗∗

(0.00598) (0.00601) (0.00598) (0.00629) (0.00604) (0.00631)

Age -0.000161 -0.000289 -0.000469 -0.00312∗ -0.00145 -0.00305∗

(0.00144) (0.00145) (0.00144) (0.00144) (0.00145) (0.00144)

Age sq -0.0000966∗∗∗ -0.0000953∗∗∗ -0.0000935∗∗∗ -0.0000614∗∗∗ -0.0000788∗∗∗ -0.0000624∗∗∗

(0.0000170) (0.0000172) (0.0000170) (0.0000171) (0.0000172) (0.0000171)

FTB -0.0148∗ -0.0343∗∗∗ -0.00990 -0.00248 0.00691 -0.00273(0.00614) (0.00616) (0.00615) (0.00621) (0.00621) (0.00621)

LIR -0.0729∗∗∗ -0.0517∗∗∗ -0.0793∗∗∗ -0.0854∗∗∗ -0.0789∗∗∗ -0.0565∗∗∗

(0.00891) (0.00895) (0.00893) (0.00905) (0.00902) (0.00906)

LVR 0.00515 0.0105 -0.00560 -0.110∗∗∗ -0.00894 -0.0273(0.0141) (0.0142) (0.0141) (0.0143) (0.0143) (0.0142)

Repayment -0.0547∗∗∗ -0.0130∗ -0.0632∗∗∗ -0.0790∗∗∗ -0.0629∗∗∗ -0.0853∗∗∗

Mortgage (0.00514) (0.00519) (0.00514) (0.00518) (0.00519) (0.00518)

κ1 1.492∗∗∗ 1.256∗∗∗ 1.548∗∗∗ 0.172∗ 1.885∗∗∗ 0.653∗∗∗

(0.0640) (0.0648) (0.0643) (0.0779) (0.0645) (0.0674)

κ2 1.606∗∗∗ 1.372∗∗∗ 1.662∗∗∗ 0.288∗∗∗ 2.003∗∗∗ 0.769∗∗∗

(0.0640) (0.0648) (0.0643) (0.0779) (0.0646) (0.0674)N 280654 280654 280654 280654 280654 280654χ2 14771.5 20487.1 14866.3 20685.3 25926.4 20576.0DF 17 17 17 17 17 17LL -216156.2 -213298.4 -216108.8 -213199.3 -210578.8 -213254.0LL 0 -223542.0 -223542.0 -223542.0 -223542.0 -223542.0 -223542.0Results of ordered probit model of choice between: variable; fixed for up to 1 year; fixed for more than 1 year.(Standard errors in parentheses). Significance denoted by:∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001. DF=degrees of freedom; LL= Log Likelihood

27

5 RESULTS

The log of income has a negative and significant coefficient, suggesting thatthose with higher income are less risk-averse. We consider this to be a key resultbecause it is filling a gap left by lab-based research. The effect of subjects’ in-come has been keenly pursued in laboratory settings. However, it is not possibleto assume, in the lab, that “outside” income is incorporated into the decision-making process; if this is assumed, it becomes impossible to explain the levelsof risk-aversion observed in the lab, a point made by Rabin (2000). In the con-text of our natural experiment, however, it is natural to assume that income isembedded in the decision-making process, since the subject is fully aware of themonthly payments that will arise as a result of their choice, and that they will bemade directly out of their monthly income. Therefore the strong income effectthat we see in Table 4 can be viewed as concrete evidence of the effect of incomeon risk-aversion.

The negative coefficient of the dummy for “self-certified income” suggests thatborrowers who “self-certify” that is, who do not (or perhaps are unable) to pro-vide proof of income, are less risk-averse. Given that self-certifiers tend to beself-employed, this result is consistent with results from empirical labour eco-nomics (see, for example Elkelund et al., 2005 and Masclet et al., 2009) to theeffect that risk-seeking individuals tend to select into self-employment.

The number of males and the number of females in the borrowing agreementappear as explanatory variables; both of these variables range from zero to four(see Table A1). It is seen that both have positive coefficients, indicating that themore people in a decision-making unit bring about higher levels of risk aver-sion. This is broadly consistent with results from work on group (mixed gender)decision-making such as Masclet et al., (2009) and Bateman and Munro (2005).Moreover, the coefficient for the number of females in Table 4 is significantlygreater than that of the number of males, indicating that females are more riskaverse than males. This is a further development to the existing literature onthe role of gender in financial decision making where Jianakoplos and Bernasek(1998) find single women to be more risk averse than couples or single men,while Dwyer et al., (2002) find that such effects are attenuated when specialistknowledge is taken into account.

28

6 CONCLUSION

Age of main borrower, and its square, are included. Both have negative coeffi-cients, the latter significantly so. This indicates that older borrowers are less riskaverse, or that the accumulation of general life experience (as proxied by age)brings about a reduction in risk aversion. This result is in agreement with Har-rison et al (2007), who find that 40-50 olds are the least risk-averse age group.Experience that is more specific to the choice task is captured by the “first-time-buyer” dummy, but this effect shows no significance.

Finally, loan-to-income ratio and loan-to-value ratio each provide a measure ofthe risk that is being taken by the borrower. The higher these ratios are, the morerisk is being taken in terms of the amount borrowed. It is therefore not surpris-ing that both have negative coefficients in model 6. It appears that those who arerisk-seeking in their borrowing behaviour are also risk seeking when they cometo make the choice between a variable and a fixed rate.

6 Conclusion

The market for mortgages is a highly topical research area at present, not leastbecause it has frequently been identified as the root cause of the global phe-nomenon that has come to be known as the “credit crunch”. In this paper, wehave considered one aspect of this market: borrowers’ choices over whether andfor how long to fix the interest rate. As discussed in Section 2, these decisions,when considered in aggregate, have profound effects, for example by fosteringstability in the housing market, and ultimately stability in the economy at large.

In this paper, we have treated the fixing decision as a risky-choice problem inthe behavioural economist’s sense. We have analysed a large-scale data set con-taining the fixing decisions of borrowers, in order to estimate the determinantsof this decision. The data set has been treated as a natural field experiment, aclassification that is justified mainly on the basis that “subjects” are, in a naturalenvironment, undertaking a task that is very similar to the sort of tasks performed

29

6 CONCLUSION

by subjects in risky choice experimental settings. A significant advantage thatthis study holds over other natural field experiments on risky choice is that theparticipating subjects have self-selected only to the extent that they are purchas-ing a home; they have certainly not self-selected on any basis that relates to theirrisk-attitude. An advantage of this study over typical laboratory studies on riskychoice, is the huge sample size. Many interesting effects that have eluded labo-ratory researchers have been estimated with very high precision in this study, byvirtue of the large sample.

An important theme of the paper has been the need to deal with the variouseconometric problems that arise as a consequence of the data being collectedin the setting of a natural field experiment rather than in that of a laboratory.These problems were: missing counterfactuals; selection bias; and endogeneity.A sequence of models have been estimated that address each of these issues indifferent combinations. The model that deals with all three problems, and istherefore preferred on theoretical grounds, is Model 6. It was the results of thismodel that were interpreted in Section 5.

In order to interpret the coefficients of the demand equation in terms of effects onrisk attitude, it has been necessary to control for the roles of interest rate expecta-tions and discounting. For interest rate expectations, the identifying assumptionwe have used is that all borrowers have expectations that correspond to marketexpectations that can be deduced from the prevailing term structure of interestrates. For discounting, interaction variables have been introduced which allowthe impact of interest rate expectations to vary between borrowers.

Most of the results relating to risk attitude appeared to have natural interpre-tations, and in addition some offered support to results, either experimental orfield-based, appearing elsewhere in the literature. Moreover, some results havebeen interpreted as providing a link between the laboratory and the frontiers ofknowledge on risky choice. The most important results in this regard are thepostive impact of pay-offs on risk aversion, and the negative effect of income.

30

7 APPENDIX

7A

ppen

dix

Tabl

eA

1:D

ESC

RIP

TIV

EST

AT

IST

ICS

FOR

DU

MM

YE

XPL

AN

ATO

RYVA

RIA

BL

ES

Year

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

Total

Obs

18,4

2523

,915

26,6

3322

,576

30,2

6033

,419

30,2

3329

,365

29,7

3736

,091

280,

654

Fco

uple

132

146

145

118

137

144

139

135

171

230

1,49

7M

coup

le11

011

312

089

129

128

131

166

182

290

1,45

8H

coup

le11

,495

14,6

5816

,277

13,4

7617

,603

18,9

5117

,095

17,3

2317

,233

20,3

6216

4,47

3R

epay

men

t2,

975

5,16

56,

705

7,26

511

,620

13,1

3612

,872

13,5

7517

,809

24,8

6411

5,98

6D

isco

unt

12,6

0714

,463

15,2

9515

,535

17,4

0616

,175

14,3

6417

,326

18,7

9113

,260

155,

222

Self

cert

’d6,

080

9726

12,1

0810

480

13,5

5315

153

13,6

3810

550

11,2

6725

897

1284

52#fem

ales

03,

844

4,96

05,

478

5,00

07,

456

8,80

87,

930

6,72

47,

014

9,14

566

,359

114

,420

18,7

7520

,968

17,4

3022

,632

24,4

1322

,136

22,4

6922

,503

26,4

7021

2,21

62

160

177

182

145

169

194

167

170

217

387

1,96

83

11

51

34

02

370

904

02

00

00

00

019

21#males

03,

039

4,24

04,

821

4,05

15,

137

5,56

65,

126

5,25

35,

402

6,30

548

,940

115

,255

19,5

2621

,656

18,4

1124

,957

27,6

7424

,912

23,9

0924

,097

29,2

3822

9,63

52

130

145

150

112

161

176

186

201

234

452

1,94

73

12

52

43

92

377

108

40

21

01

00

01

1924

Not

e: •Fi

gure

sgi

ven

are

the

num

bero

fobs

erva

tions

whe

reth

edu

mm

yva

riab

leis

equa

lto

one.

•“F

”“M

”an

d“H

”re

fert

oFe

mal

e,M

ale

and

Het

eros

exua

lcou

ples

resp

ectiv

ely.

31

7 APPENDIX

Tabl

eA

2.1:

DE

SCR

IPT

IVE

STA

TIS

TIC

SFO

RE

XPL

AN

ATO

RYVA

RIA

BL

ES

Year

1992

1993

1994

NMean

Stddev

NMean

Stddev

NMean

Stddev

Adv

ance

18,4

2543

,617

.73

24,6

52.0

123

,915

44,2

25.2

324

,806

.30

26,6

3346

,435

.47

27,7

97.2

7Pr

ice

18,4

2561

,208

.19

41,0

01.1

523

,915

61,6

64.6

139

,961

.04

26,6

3363

,998

.95

43,0

90.9

1In

com

e18

,425

20,8

00.0

013

,157

.40

23,9

1521

,003

.17

13,3

82.1

526

,633

21,6

79.2

214

,110

.89

Age

18,4

2534

.22

10.9

123

,915

34.6

710

.86

26,6

3335

.12

11.0

8r

18,4

259.

251.

1823

,915

5.79

0.19

26,6

335.

350.

31p v

13,9

709.

530.

9911

,493

7.12

1.10

15,4

815.

881.

57p f(<

1yr)

1,06

18.

871.

142,

276

6.66

0.81

1,06

24.

592.

21p f(>

1yr)

3,39

49.

581.

0410

,146

7.32

0.82

10,0

906.

720.

99L

IR18

,425

2.24

0.79

23,9

152.

260.

7326

,633

2.28

0.74

LVR

18,4

250.

780.

2223

,915

0.77

0.22

26,6

330.

780.

22S

Fem

ale

2,90

635

.26

12.6

44,

092

34.5

211

.67

4,67

135

.42

12.2

1S

Mal

e3,

733

32.5

310

.13

4,84

632

.71

9.87

5,35

232

.98

10.0

6SF

FTB

1,80

732

.94

12.5

52,

700

32.0

811

.13

3,10

032

.69

11.6

1SM

FTB

2,48

830

.58

9.64

3,31

430

.55

8.85

3,89

530

.76

8.99

FTB

Age

9,46

931

.40

10.7

712

,775

31.7

210

.49

14,5

7832

.03

10.6

2

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e: •M

onet

ary

vari

able

s:“A

dvan

ce”

“Pri

ce”

and

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are

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FTB

”(S

ingl

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ime

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),“

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fort

hese

isth

em

ean

ofag

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ars)

fort

here

leva

ntgr

oup.

32

7 APPENDIX

Tabl

eA

2.2:

DE

SCR

IPT

IVE

STA

TIS

TIC

SFO

RE

XPL

AN

ATO

RYVA

RIA

BL

ES

Year

1995

1996

1997

NMean

Stddev

NMean

Stddev

NMean

Stddev

Adv

ance

22,5

7647

,487

.00

28,1

54.5

730

,260

51,1

75.0

831

,889

.67

33,4

1955

,307

.95

35,6

95.9

8Pr

ice

22,5

7663

,846

.62

43,2

90.6

030

,260

70,3

14.1

849

,435

.67

33,4

1977

,056

.78

56,1

59.3

1In

com

e22

,576

22,2

79.6

214

,527

.35

30,2

6024

,655

.77

17,0

24.3

733

,419

26,2

22.5

118

,424

.50

Age

22,5

7634

.46

10.6

830

,260

35.1

210

.49

33,4

1935

.45

10.2

9r

22,5

766.

570.

1430

,260

5.87

0.16

33,4

196.

640.

49p v

16,6

076.

041.

7124

,137

5.39

1.54

19,6

436.

661.

41p f(<

1yr)

457

5.30

2.12

814

4.68

1.71

667

6.28

1.32

p f(>

1yr)

5,51

26.

541.

225,

309

6.37

1.33

13,1

097.

060.

92L

IR22

,576

2.28

0.73

30,2

602.

240.

7733

,419

2.27

0.83

LVR

22,5

760.

800.

2130

,260

0.79

0.22

33,4

190.

780.

22S

Fem

ale

3,93

334

.71

11.6

34,

998

35.0

011

.30

5,42

035

.15

11.0

8S

Mal

e4,

909

32.8

79.

807,

325

33.5

59.

438,

678

33.9

19.

15SF

FTB

2,47

031

.43

10.1

92,

920

31.1

99.

663,

073

31.5

99.

73SM

FTB

3,36

530

.57

8.65

4,62

130

.69

8.15

5,08

530

.91

8.06

FTB

Age

12,0

8330

.90

9.48

14,7

2730

.96

9.04

15,3

2431

.47

9.17

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here

leva

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33

7 APPENDIX

Tabl

eA

2.3:

DE

SCR

IPT

IVE

STA

TIS

TIC

SFO

RE

XPL

AN

ATO

RYVA

RIA

BL

ES

Year

1998

1999

2000

NMean

Stddev

NMean

Stddev

NMean

Stddev

Adv

ance

30,2

3358

,387

.05

37,6

48.9

129

,365

65,7

52.6

144

,834

.98

29,7

3771

,193

.24

50,3

28.4

0Pr

ice

30,2

3382

,603

.34

59,8

27.4

829

,365

93,9

23.4

969

,896

.46

29,7

3710

2,44

9.30

78,2

03.6

2In

com

e30

,233

27,4

04.2

219

,229

.83

29,3

6530

,151

.89

21,4

77.7

829

,737

31,5

48.1

122

,404

.20

Age

30,2

3335

.44

10.1

729

,365

35.8

910

.22

29,7

3736

.40

10.8

3r

30,2

337.

230.

3429

,365

5.28

0.25

29,7

375.

980.

06p v

12,9

286.

802.

1917

,321

5.69

1.26

18,4

656.

011.

15p f(<

1yr)

372

6.72

1.47

789

5.59

1.19

1,89

95.

960.

67p f(>

1yr)

16,9

336.

730.

7711

,255

5.85

0.89

9,37

36.

380.

85L

IR30

,233

2.28

0.79

29,3

652.

330.

8029

,737

2.38

0.79

LVR

30,2

330.

770.

2329

,365

0.76

0.22

29,7

370.

750.

22S

Fem

ale

4,98

735

.27

10.8

75,

117

35.5

410

.61

5,23

036

.30

11.3

7S

Mal

e7,

793

34.0

69.

126,

556

34.1

09.

526,

829

34.8

610

.16

SFFT

B2,

947

31.9

49.

502,

950

32.1

29.

242,

912

33.1

410

.86

SMFT

B4,

807

31.4

88.

374,

189

31.7

08.

524,

142

32.4

810

.05

FTB

Age

14,6

2231

.80

9.16

13,8

7332

.29

9.19

13,5

1833

.12

10.9

4

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and

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curr

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rstT

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),“

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SM

ale

(Sin

gle

Mal

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are

alla

lldu

mm

yva

riab

les;

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mea

nsgi

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fort

hese

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ean

ofag

e(i

nye

ars)

fort

here

leva

ntgr

oup.

34

7 APPENDIX

Tabl

eA

2.4:

DE

SCR

IPT

IVE

STA

TIS

TIC

SFO

RE

XPL

AN

ATO

RYVA

RIA

BL

ES

Year

2001

Total

NMean

Stddev

NMean

Stddev

Adv

ance

36,0

9173

,311

.02

54,2

73.2

428

0,65

457

,102

.21

40,1

52.7

5Pr

ice

36,0

9111

6,54

2.30

88,7

34.8

628

0,65

481

,806

.41

64,1

93.2

4In

com

e36

,091

34,4

48.1

228

,468

.19

280,

654

26,6

65.0

320

,016

.55

Age

36,0

9136

.04

8.09

280,

654

35.3

810

.32

r36

,091

5.00

0.62

280,

654

6.17

1.16

p v22

,832

5.31

0.96

172,

877

6.28

1.80

p f(<

1yr)

2,11

75.

470.

8011

,514

6.05

1.67

p f(>

1yr)

11,1

425.

760.

6796

,263

6.66

1.17

LIR

36,0

912.

280.

9228

0,65

42.

290.

80LV

R36

,091

0.69

0.26

280,

654

0.76

0.23

SFe

mal

e6,

049

35.7

28.

6147

,403

35.3

311

.11

SM

ale

8,82

334

.98

7.42

64,8

4433

.83

9.39

SFFT

B2,

771

31.8

18.

1527

,650

32.0

710

.26

SMFT

B4,

110

31.3

57.

4640

,016

31.1

58.

65FT

BA

ge13

,197

31.7

28.

1313

4,16

631

.75

9.71

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FTB

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ime

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er),

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),“

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ingl

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mal

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SM

ale

(Sin

gle

Mal

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are

alla

lldu

mm

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riab

les;

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mea

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fort

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isth

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e(i

nye

ars)

fort

here

leva

ntgr

oup.

35

7 APPENDIX

Table A3:OLS AND HECKMAN PRICE EQUATIONS FOR MODELS 3 TO 6

OLS OLS Heckman HeckmanFixed V ariable F ixed V ariable

MainLog of -0.106∗∗∗ -0.144∗∗∗Advance (0.00618) (0.00604)

Female 0.0122 0.182∗∗ 0.0534 0.180∗∗Couple (0.0739) (0.0686) (0.0745) (0.0688)

Male -0.00167 0.178∗ 0.0148 0.144∗Couple (0.0741) (0.0691) (0.0748) (0.0693)

Hetero 0.0437 0.117∗ 0.0776 0.0809Couple (0.0596) (0.0526) (0.0601) (0.0528)

Single -0.0728 0.129∗ -0.0000151 0.163∗∗Female (0.0600) (0.0531) (0.0605) (0.0532)

Single -0.0750 0.000143 -0.0352 0.00901Male (0.0599) (0.0529) (0.0604) (0.0530)

Loan to 0.00801 -0.0124∗ -0.00107 -0.0665∗∗∗Income Ratio (0.00476) (0.00485) (0.00460) (0.00456)

Loan to -0.00500 0.174∗∗∗ 0.0213 0.0730∗∗∗Value Ratio (0.0160) (0.0152) (0.0163) (0.0151)

Repayment 0.00243 0.0344∗∗∗ -0.00789 0.0245∗∗∗Mortgage (0.00666) (0.00685) (0.00674) (0.00686)

Distmort -0.322∗∗∗ -1.091∗∗∗ -0.388∗∗∗ -1.068∗∗∗Mortgage (0.00639) (0.00681) (0.00730) (0.00734)

r 0.807∗∗∗ 0.877∗∗∗ 0.805∗∗∗ 0.886∗∗∗(0.00374) (0.00278) (0.00377) (0.00277)

s 0.251∗∗∗ 0.244∗∗∗(0.00413) (0.00418)

s2 -0.0924∗∗∗ -0.0887∗∗∗(0.00262) (0.00262)

s3 0.0270∗∗∗ 0.0263∗∗∗(0.000950) (0.000950)

Constant 2.927∗∗∗ 2.852∗∗∗ 1.536∗∗∗ 1.387∗∗∗(0.0918) (0.0819) (0.0663) (0.0565)

Cont’d

36

7 APPENDIX

Table A3. Continued: HECKMAN SELECTION EQUATIONS FOR MODELS 5 AND 6OLS Fixed OLS Variable Fixed V ariable

Selection Fix NofixFemale N/A N/A 0.201∗∗∗ -0.204∗∗∗Couple N/A N/A (0.0549) (0.0548)

Male N/A N/A 0.126∗ -0.132∗Couple N/A N/A (0.0551) (0.0551)

Hetero N/A N/A 0.223∗∗∗ -0.226∗∗∗Couple N/A N/A (0.0432) (0.0432)

Single N/A N/A 0.256∗∗∗ -0.254∗∗∗Female N/A N/A (0.0435) (0.0435)

Single N/A N/A 0.157∗∗∗ -0.158∗∗∗Male N/A N/A (0.0434) (0.0434)

Age N/A N/A -0.00813∗∗∗ 0.00827∗∗∗N/A N/A (0.000279) (0.000281)

Self Cert’d N/A N/A -0.339∗∗∗ 0.335∗∗∗Mortgage N/A N/A (0.00500) (0.00514)

First Time N/A N/A 0.0324∗∗∗ -0.0143∗Buyer N/A N/A (0.00584) (0.00589)

Log of N/A N/A 0.192∗∗∗ -0.174∗∗∗Advance N/A N/A (0.00491) (0.00501)

Loan to N/A N/A 0.0533∗∗∗ -0.0577∗∗∗Income Ratio N/A N/A (0.00367) (0.00368)

Loan to N/A N/A 0.0730∗∗∗ -0.0962∗∗∗Value Ratio N/A N/A (0.0140) (0.0140)

Repayment N/A N/A -0.0633∗∗∗ 0.0612∗∗∗Mortgage N/A N/A (0.00524) (0.00525)

Distmort N/A N/A -0.341∗∗∗ 0.342∗∗∗Mortgage N/A N/A (0.00500) (0.00501)

r N/A N/A -0.0689∗∗∗ 0.0701∗∗∗N/A N/A (0.00251) (0.00251)

s N/A N/A -0.0881∗∗∗ 0.0896∗∗∗N/A N/A (0.00201) (0.00200)

Constant N/A N/A -1.643∗∗∗ 1.465∗∗∗N/A N/A (0.0713) (0.0720)

Cont’d

37

REFERENCES REFERENCES

Table A3. Continued:SUMMARY REPORT FOR OLS AND HECKMAN PRICE EQUATIONS

OLS OLS Heckman HeckmanFixed V ariable F ixed V ariable

Rho N/A N/A 0.251∗∗∗ 0.0876∗∗∗(0.0114) (0.0107)

Sigma N/A N/A 0.0419∗∗∗ 0.318∗∗∗(0.00287) (0.00178)

N 107777 172877 280654 280654χ2 52586.9 122039.0Degrees of freedom 14 11 13 10Log likelihood -155119.1 -299626.3 -332549.0 -477360.7Log likelihood zero -177128.2 -346529.1R2 0.335 0.419Dependent variable in main equation Interest Rate (fixed or variable as appropriate).Dependent variable in Heckman Selection equation Fix or No fix (as appropriate).(Standard errors in parentheses). Significance denoted by:∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

Note: that the base case for couple-type/ single category in the OLS and Heck-man (main and selection stages) models is multiple occupancy households i.e.three or more signatories to the mortgage, the number of observations for theseis 3,934.

References

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[2] BACON, P. M. (2009) “Tenure Choice, Mortgage Choice and Lender Behaviour in theHousing Market of England and Wales”, Unpublished Ph.D Thesis, UEA, Norwich, UK.

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[6] BRUECKNER, J. K. and J. R. FOLLAIN (1988): “The Rise and Fall of the A.R.M: AnEconometric Analysis of Mortgage Choice”, The Review of Economics and Statistics, 70,93-102.

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40