Instrument Choice: The Demand for Mortgages in Canada

Ž .JOURNAL OF URBAN ECONOMICS 39, 282]302 1996ARTICLE NO. 0015

Instrument Choice: The Demand for Mortgages in Canada*

JON BRESLAW AND IAN IRVINE

Department of Economics, Concordia Uni ersity, Montreal, Quebec, H3G-1M8,Canada

AND

ABDUL RAHMAN

Department of Finance, Uni ersity of Ottawa, Ottawa, Ontario, K1N-6N5, Canada

Received January 10, 1994; revised January 9, 1995

This paper is directed at understanding the factors which caused mortgagedemand to fluctuate to the degree witnessed in the 1980s. We model the mortgagechoice decision as involving simultaneous options on both the term and theamortization choice, by cost minimizing risk averse borrowers. The model isestimated using a bivariate ordered probit methodology. An extensive databasecontaining details on the financial and demographic characteristics of householdsis used. We find that, contrary to the dominant model of mortgage demand,borrowers react to market conditions in a risk averse and cost minimizing manner.Q 1996 Academic Press, Inc.

1. INTRODUCTION

Prior to the 1980s, the suppliers of mortgage funds relied mainly on aŽ .standard fixed-rate mortgage FRM , with contract terms of 5 years in

Canada, and as long as 25 years in the United States. The rising and morevolatile interest rates in the 1970s created significant duration risk expo-sure as the portfolios of financial intermediaries were rendered unbal-anced. In an effort to hedge this duration risk, U.S. lenders introduced

Ž .adjustable rate mortgages ARM , while Canadian lenders shifted tomortgage terms ranging from 6 months to 5 years. Indeed, 3- and 1-yearterms only became widely available in Canada in 1978 and 1980, respec-

* This project was carried out with the assistance of a financial contribution from theCanada Mortgage and Housing Corporation under the terms of the External ResearchProgram. The authors thank the CMHC both for providing the data and for the financialsupport. We record our thanks to Jan Brueckner, Susan Corbeille, Mark McInnis, DenisMyette, Gordon Fisher, Doug Wilson and two anonymous referees for helpful discussions andcomments. The views expressed are those of the authors and do not represent the view of theCMHC.

282

0094-1190r96 $18.00Copyright Q 1996 by Academic Press, Inc.All rights of reproduction in any form reserved.

DEMAND FOR MORTGAGES IN CANADA 283

tively. Concurrently, there was an enormous volatility in the demand formortgages of different terms in Canada, and between ARMs and FRMs inthe United States. Furthermore, as shown in Fig. 1, this volatility inmortgage terms was accompanied by large fluctuations in the amortizationperiod chosen.

This paper is directed at understanding the factors which caused mort-gage instrument choice to fluctuate to the degree that has been evidenced.To this end, we model the mortgage choice problem as a joint decision, byrisk averse cost minimizing agents, involving options on both the term andthe amortization period. Modeling the decision process in this way enablesus to explain the observed patterns of the 1980s in the Canadian mortgagemarket. As we explain in Section 3, these are difficult to understand in thecontext of choice models which focus upon the term and amortizationdecisions separately.

We have a very large data base spanning nine years, comprising over750,000 observations on Canadian households, with extensive details onboth financial and demographic characteristics. This database was com-

Ž .piled by the Canada Mortgage and Housing Corporation CMHC andconsists of all borrowers who require mortgage insurance. Furthermore,because the data span several years which involve major swings in thehousing market, as well as in the economic environment, they provide agood basis for estimating an econometric model.

Ž .In addition, for the period we study 1980]1988 , the choices available inthe Canadian mortgage market are more clearly defined than in theUnited States. Specifically, the choice between an ARM and an FRM in

FIG. 1. Five-year term r 25q year amortization. Three month moving average.

BRESLAW, IRVINE, AND RAHMAN284

the U.S. market is considerably more complex than just being a binaryw xdecision. Peek 12 has pointed out that there have existed as many as 400

types of ARM in the United States. In contrast, the Canadian rollovermortgage essentially involves choices over the length of the amortizationperiod, typically 5 to 30 years, and the term of the mortgage, typically 6months to 5 years.1

Our results indicate that borrowers, rather than purchasing a homewhich places them in a position of being strongly bound by a mortgagepayment constraint, leave themselves considerable latitude in the choice ofthe term and amortization of their mortgage. That is, typical debt service

Ž . Ž .to income GDSY payments and loan to value LTV ratios are not undulyhigh, and consequently borrowers can respond in a risk averse and costminimizing manner to changes in interest rates and other variables.

The paper is organized as follows. In Section 2 we present a literaturereview. The theory underlying our mortgage choice model and the econo-metric specification of the model is described in Section 3. In Section 4, wedescribe the data and present summary statistics. The empirical findingsare presented and discussed in Section 5, and concluding remarks aregiven in Section 6.

2. REVIEW OF THE LITERATURE

The mortgage choice problem involves two main decisions: the maturityor amortization decision, and the term decision. The loan maturity deci-sion is determined both by household characteristics and by marketvariables. Econometrically, such variables are seen as determining theprobability that a borrower will choose a particular amortization period.

w xPhillips, et al. 13 showed that relative cost and life cycle effects, proxiedby age, are significant determinants of maturity choice for fixed-ratemortgage borrowers. They found that the probability of a shorter loanmaturity increases at an increasing rate with age; this may reflect the life

w xcycle effect of reduced income levels in retirement years. Dhillon et al. 6also considered the FRM maturity decisions. Using a probit model on a

1 There are further significant institutional differences between Canadian and U.S. mort-gage markets. For example, Canadian home-owners cannot deduct mortgage interest whencomputing taxable income. Furthermore, prepayment remains easier in Canada than in theUnited States due to the shorter terms on mortgage contracts. For example, if a borrowerchooses a 3 year term at a fixed interest rate and a 25 year maturity, the borrower can prepayas much of the capital as desired at the end of the 3 year term, without penalty. In addition,in recent years, many lenders permit borrowers to prepay 10% of the capital borrowed eachyear, within the term of the contract; amounts in excess of this are subject to penalty. Theflexibility which these institutional arrangements afford the borrower means that the likeli-hood of prepayment plays a reduced role in the mortgage instrument choice.


national sample for 1985 and 1986, they found that maturity choice isdetermined by relative tax rates, relative cost, regional housing prices, andlife cycle variables such as income and age.

The term decision deals with the determinants of the probability that aborrower will choose between an FRM and an ARM. The theoretical

w xstudies which have addressed this problem include Alm and Follain 1 ,w x w x w xBrueckner 2 , Brueckner and Follain 3 , and Dhillon et al. 5 and are

w xsummarized in Follain 7 . The general conclusion of these studies is thatthe important determinants of instrument choice are the level of interestrates and the spread between FRM and ARM rates.

w xRecently, Phillips and Vanderhoff 14 found evidence suggesting thatinstrument choice is significantly affected not only by the FRM]ARM ratedifferential, but also by the initial discount on the ARM rate. As withmany previous studies, they found that instrument choice is dominated byprice related factors and that demographic variables have less influence.

Few studies, however, deal with joint decision making over more than aw xsingle choice. An exception is Capone and Cunningham 4 , who developed

and estimated a recursive model of prepayment and instrument choice.They found that the expected holding period, for a given level of risktolerance, affects instrument choice. This gives a significant role to ex-pected prepayment in the mortgage choice decision. Since the degree ofthe borrower’s risk aversion is central to the mortgage choice decision, anyexplanatory variable which tends to lower the borrower’s degree of riskaversion will increase the probability of an ARM choice. A second excep-

w xtion is Sa-Aadu and Sirmans 15 who examine the choice between FRMsand several different types of ARM. With these exceptions, the literaturehas modeled choices in a way which does not adequately reflect thesimultaneous options on term and amortization faced by borrowers.

3. A THEORY OF MORTGAGE CHOICE

3.1. Behaïoral Model

The optimization theory underlying discrete choice models is well known.w xIt was developed by McFadden 11 and others, and has been applied to

many different problems, one of which is mortgage choice. Essentially, theprobability of choosing one option over another depends upon which yieldsthe higher utility.

The utility maximization problem facing a home buyer is complex: theoptimal amount of housing must be chosen in conjunction with an appro-priate mortgage instrument, each subject to income constraints and uncer-tainty about the future. Our model is similar to that commonly proposed inthe literature in that the mortgage demand is conditioned on the purchaseof a property of a given price. We propose that borrowers are risk averse,


and that they maximize a utility function U which is defined by

U s U C , R : Z U X - 0 U X - 0, 1Ž . Ž .C R

where C denotes the discounted lifetime cost of the mortgage, R is thedegree of risk associated with the mortgage, and Z is a set of variablesreflecting tastes, income, risk aversity, and expectations.

Ž .C depends upon the term chosen since the yield curve is rarely flat ,and the amortization period:

C s C A , T CX ) 0 CX ) 0. 2Ž . Ž .A T

A short term reduces cost because short rates are generally less than longrates. A shorter amortization yields a smaller present discounted value ofinterest payments because the rate at which individuals discount futurepayments is generally less than the mortgage rate. This difference betweenthe borrower’s own rate of discount and the mortgage rate is crucial in acost minimizing approach. Were these rates equivalent, then the lifetimecost of a 30 year mortgage would be the same as a 20 year mortgage. In

Žgeneral, one would expect borrowers to have a discount rate or opportu-.nity cost that is less than the mortgage rate, and thus have an incentive to

choose a shorter amortization period, ceteris paribus. Conversely, if thediscount rate exceeds the mortgage rate, a long amortization would bepreferred.2 A decrease in life cycle cost can thus be achieved by decreasingterm or by decreasing the amortization period. However, a more bindingpayment constraint may require a long amortization and thus restrict theborrower’s ability to minimize life cycle costs.

R has two components}the risk associated with uncertain future inter-est rates during the holding period and the risk associated with incomevariation over the amortization period.

R s R A , T RX - 0 RX - 0 3Ž . Ž .A T

The desire to avoid the risk associated with fluctuating mortgage rates is akey elements in the borrower’s choice. Risk can be reduced by increasingthe term or the amortization period. Again, the stronger the paymentconstraint, the more likely that a risk averse borrower who chooses a longterm will also choose a long amortization, since the increased monthlypayments associated with the longer term are moderated by the longeramortization period.

2 This observation does not imply that borrowers would necessarily prefer extremely shortamortization periods. Such corner choices would not maximize lifetime utility in the moregeneral context, because they would unbalance the overall intertemporal consumption

w xallocations of households. Schwab 16 and others have developed these ideas fully.


C and R are not independent: the choice of a longer term, T , willincrease monthly payments, M, if the yield curve is positive; this can bemitigated by taking a longer amortization, A. Formally,

M s M A , T F K M X - 0 M X ) 0, 4Ž . Ž .A T

Ž .where K is a constraint on e.g., monthly payments, depending uponincome.

The behavioral outcome depends crucially on the relative importance ofcost minimization as opposed to risk aversion. One extreme, which wedesignate Type I behavior, occurs when payment constraints become

Ž .strongly binding: that is, the gross debt service to income ratio GDSYapproaches the maximum permitted level. In this situation, monthly pay-ments are minimized by selecting a short term and a long amortizationperiod. While this implies that the total cost of the mortgage will be high,since it is held for so long, this choice does at least permit the borrower toservice the debt. By contrast, in Type II behavior where the monthlypayment constraint is less binding, a borrower has the latitude to choose a

Ž . Ž . 3longer term if risk averse and a shorter amortization if a cost minimizer .The simultaneous nature of the term and amortization choices follows

directly. For any given amortization, the choice of term is determined fromthe present value optimizing time path of monthly cost and risk. Thisimplies that term is endogenous. On the other hand, the principal reasonfor shortening the amortization period is to reduce the life cycle cost ofthe mortgage, which itself depends upon the term chosen. This implies thatamortization is also endogenous. Hence both term and amortization aresimultaneously determined. Thus, one can either model the simultaneousstructural system after having imposed identification restrictions, or onecan model the reduced form system. We adopt the latter approach here,since the reduced form facilitates a comparison with the existing literature.

The ability of the borrower to significantly influence his or her mortgagepayments on a given house purchase by choosing the term and amortiza-tion period leads to a variety of outcomes which are not feasible in a morerestricted framework. In particular, the widely cited work of James Kearlw x w x8 and Robert Schwab 16 implies that, during inflationary periods whichare accompanied by higher nominal interest rates, the real value ofmortgage payments is ‘‘tilted’’ toward the early part of the repaymentsschedule. This tilting reduces the borrower’s ability to sustain a given

3 Of course, a risk neutral borrower in a Type II situation would choose a shorter termthan a risk averse borrower and this would further shorten the amortization period.


TABLE 1Mortgage Distribution by Term and Amortization

Term: 1 year 2]4 years 5 years

Amortization: - 25 25 q - 25 25 q - 25 25 q

1980 16% 24 84% 121 13% 25 87% 169 13% 68 87% 4611981 28% 63 72% 163 20% 52 80% 206 20% 56 80% 2301982 55% 207 45% 168 41% 168 59% 245 36% 42 64% 741983 43% 139 57% 185 37% 178 63% 301 41% 69 59% 1011984 34% 107 66% 211 39% 167 61% 266 38% 81 62% 1301985 34% 84 66% 162 35% 129 65% 236 32% 108 68% 2261986 31% 71 69% 159 28% 78 72% 198 37% 152 63% 2641987 32% 72 68% 156 28% 87 72% 224 28% 103 72% 2611988 29% 73 71% 180 25% 81 75% 241 27% 89 73% 244

Note. Percentage are row percentages by term, counts are sample count per cell.

monthly payment, and therefore borrowers should either purchase lesshousing or extend the amortization period of their mortgage. However, anextended amortization is not what is observed in such periods. For exam-

Ž .ple, Table 1 illustrates that in 1982 a year of extremely high interest ratesthere was a sharp reduction in the percentage of borrowers choosing long

Ž .amortization periods G 25 years . Among borrowers who chose 1 yearterms, 55% chose amortization periods of less than 25 years, whereas only16% of borrowers made such a choice in 1980. Similar patterns are inevidence for each of the three term categories. This suggests that lifecyclecosts may play a significant role in mortgage choice, and that higher ratesmay not necessarily result in longer amortization, as implied by Type Ibehavior.

3.2. An Econometric Specification

Econometrically, we specify the term and amortization choices to beŽ .determined by vectors of market financial MKTFIN , individual financial

Ž . Ž . Ž .INDFIN , demographic DEMOG , and other OTHER variables. In addi-tion, the term choice will be influenced by the amortization period se-lected, and the amortization choice by the term. Thus the structural systemŽ .before imposing identification restrictions is

TERMs T MKTFIN, INDFIN, DEMOG, OTHER, AMORT, h 5Ž . Ž .1

AMORTs A MKTFIN, INDFIN, DEMOG, OTHER, TERM, h . 6Ž . Ž .2


The theory underlying the role for these variables has been well devel-oped in the literature in the univariate case}for example, Brueckner and

w x w xFollain 3 or Capone and Cunningham 4 for the ARMrFRM choice andw x w xDhillon et al. 6 or Phillips et al. 13 for the amortization choice.

Ž . Ž .Consistent estimation of the parameters in Eqs. 5 and 6 must takeinto account the endogeneity of some of the right-hand side variables. Inparticular, the individual financial variables include the GDSY and the LTVratio, both of which are partly determined by the term and amortizationdecisions themselves. Since our focus is the responsiveness of term andamortization to changes in the economic environment, we estimate a twoequation reduced form system for term and amortization, where each isexpressed solely as a function of the exogenous variables.

Neither of the two endogenous variables is continuous. For the termdecision, the applicant chooses the number of years from the set ofintegers between one and five. An approach to modeling this is to assume

Ž .a latent, unobserved variable desired term and a categorical observedŽ .indicator the term selected . In the present context, since relatively few

Ž .applicants chose 2 or 4 year terms 7.3% and 2.5%, respectively , weŽ . Žaggregate into three categories}short 1 year, 28.8% , medium 2 to 4

. Ž .years, 37.4% , and long 5 years, 33.8% . Similarly, although the amortiza-tion period chosen can range from 1 to 40 years, applicants limit theirchoices: 96% choose either a 15-, 20-, or 25-year period. Thus we againassume a latent variable, desired amortization period, along with a categor-ical observed indicator, the amortization period selected. Two categories

Ž . Žare considered}short less than 25 years, 31.6% and long 25 years or.longer, 68.4% . Figure 2 displays the breakdown of the term and amortiza-

tion choices observed in the sample.If the task involved only a single latent variable, then the objective

Ž .would be the efficient estimation of the k = 1 vector of b coefficients inthe stochastic single equation regression model,

yU s Xb q e , 7Ž .

U Ž .where y is an n = 1 vector of a latent dependent variable, X is anŽ . Ž .n = k matrix of independent variables, and e is an n = 1 vector ofdisturbance terms. yU is not observed; rather we observe a categoricalindicator, y. For the amortization problem, we consider two alternatives,and a standard probit estimator could be applied. For the term case, whichis trichotomous, the corresponding yU has an ordered categorical repre-jsentation, y .j

Since we have two jointly selected latent variables, a system-wide ap-proach is required for consistent parameter estimation. The simultaneous


Ž . Ž .FIG. 2. a Mortgage term. b Amortization period.

structural system for two latent endogenous variables, yU and yU , can be1 2expressed as

yU s X b q g yU q e 8Ž .1 1 1 1 2 1

yU s X b q g yU q e , 9Ž .2 2 2 2 1 2

where X and X are matrices of exogenous variables, not necessarily1 2� 4distinct, and e and e are multivariate normally distributed, e , e ª1 2 1 2

Ž .N 0, S . If the disturbance terms contain common elements, and we haveargued above that this will likely be the case in this model, then thecorrelation between the error terms, r, may be substantial. The estimation


of this type of model is well known, and is discussed in, for example,w x w xMaddala 9 and Mallar 10 .

Ž . Ž .The reduced forms of Eqs. 8 and 9 are

1 e q g e1 1 2Uy s X b q g X b q 10Ž . Ž .1 1 1 1 2 21 y g g 1 y g g1 2 1 2

s Xp q m 11Ž .1 1

1 g e q e2 2Uy s g X b q X b q 12Ž . Ž . Ž .2 2 1 1 2 21 y g g 1 y g g1 2 1 2

s Xp q m . 13Ž .2 2

To evaluate the sensitivity of mortgage choice behavior to changes inexogenous policy variables, a knowledge of the reduced form coefficients isall that is required. Consequently, we estimate the reduced form systemŽ Ž . Ž .. 4Eqs. 11 and 13 using bivariate ordered probit.

The exogenous variables of the system are described below.

Ž .a Market financial äriables}MKTFIN.

v INT5 is the 5 year average commercial bank mortgage rate.5 Wheninterest rates are high, individuals would be expected to take short termmortgages. Since the term structure is generally positively sloped, thischoice effectively reduces the cost of the mortgage. In periods when

Ž .interest rates are unusually high as in the early 1980s individuals maychoose a short term for the additional reason that rates are expected tofall in the future.

v SPREAD is the difference between the 5 the 1 year rate. A largespread implies that, for any interest rate level, households should prefer ashorter term.

v DEL5 is the month to month rate of growth of the average commer-Ž .cial bank 5 year mortgage rate. If rates are rising falling , and individuals

4 As in the standard probit model, the coefficients in the reduced form model require� 4 Ž .identification conditions. Thus m , m ª N 0, V , where1 2

1 rV s .

r 1

In an earlier version of this paper, we found that our estimates are robust to the assumptionof normality by applying a semiparametric methodology.

5 The actual interest rate charged is an endogenous variable and cannot be used withoutcausing the estimated coefficient to be biased. Accordingly, we use a typical interest rateavailable at the time of mortgage application.


form expectations by extrapolating immediate past experience, they mayŽ .prefer a long short term.

These market financial variables should influence both the term andamortization choices. In the term equation, the ability to lock into a 5 year,rather than a 1 year, contract represents a significant reduction in risk.This effect on risk must be traded off against the effect on the cost of amortgage which differences in the levels of interest rates and their spreadsimply.

In addition to a direct influence, these variables will have an impact onthe amortization choice indirectly through their influence on the termdecision. Under Type I behavior, monthly cost is paramount, so that thesame influences that force a borrower to accept a short term also result ina long amortization; thus we would perceive an inverse relationship be-tween term and amortization. Under Type II behavior, in contrast, a directrelationship between term and amortization would be expected: specifi-cally, for a given risk, an increase in rates should induce a shorter termchoice and a shorter amortization choice because, for any given personaldiscount rate, a higher mortgage rate increases lifetime cost and this canbe countered by reducing the amortization period.

Ž .b Indi idual financial äriables}INDFIN.

v LRINC is the logarithm of real family income, and is a measure ofthe borrower’s purchasing power. A higher real income should enable ahousehold to pay off its mortgage in a shorter period of time, and alsoenable it to take higher risks associated with short term rates.

v The degree to which a borrower is financially constrained is indi-cated by the values taken by LTV and GDSY. Housing price is one of thedeterminants of these variables. Accordingly, we include the logarithm of

Ž .the real price of housing LRPH as an explanatory variable. This is a trueexogenous variable since it is defined as the price of housing for eachmonth and region in the sample, rather than the price of the houseactually purchased.

Ž .c Demographic äriables}DEMOG.

v A NUCLEAR family is defined as one in which the applicant ismarried or has children, but in which there is no other dependent. If riskaversion is influenced by one’s family structure, this proxy for risk aversionshould induce households to avoid the risk of shorter terms and chooselonger terms.

v The AGE variable captures life cycle effects. To deal with possiblenonlinearities, it is specified by six categorical dummies.


Ž .d Other äriables}OTHER.

Ž .v Regional dummies RGN act as proxies for variables which might beinfluenced by the part of the country in which the household resides.

Ž .v Seasonal dummies SSN capture the influence of the time of theyear at which the household applies for a mortgage}only 15% of alltransactions occur in the last three months of the year. Households thatrelocate in this quarter are thus more likely to be more mobile than thenorm. This dummy acts as a proxy for variables which influence mobility,and thus influence mortgage choice.

v TREND is a linear variable designed to capture habit persistence andlearning.

4. DATA

Our data have been supplied by the CMHC and cover the period1980]1988. The minimum down payment was 10% of the value of theproperty; however insurance was required for any purchase where the LTVratio exceeded 75%. All mortgages in this database represent new loansand required insurance. This is an important characteristic of the database,for it means that the observed mortgage demand is jointly determined withthe purchase decision. It also provides a very simple direct test of the

Ž .dominant mortgage demand model Type I behavior . The maximumpermitted value of GDSY for these borrowers was 35%. Of these, only 9%

� 4 � 4fell in the GDSY bracket 30]35% and 28% in the 25]30% bracket. Ifthe permitted limits accurately represent what a household can afford, thispattern suggests that most households choose to stay well away from theseboundaries in their purchase decision.

A summary of the data, by year and region, is given in Table 2. Whilethe regional breakdown is roughly proportional to population size, thedistribution by application date is skewed, with the low values for1980]1983 likely reflecting the impact of high interest rates that prevailedduring this period. Since our analysis is concerned with mortgage behaviorconditional on a mortgage application having been made, a random sampleof 1000 observations per year was selected resulting in a sample set of 9000observations. This corresponds to an approximate 1% sample of the

Ž .population. The majority of these were for single dwellings 89% and forŽ .existing dwellings 80% .

We restricted the sample to the ten provinces, since economic condi-tions in the Yukon and North West Territories are not typical of Canada.We also restricted it to applicants who selected terms of 1 to 5 years


TABLE 2Summary Description of the CMHC Data Base

Date Frequency Percent Province Frequency Percent

NFD 13469 1.71980 47223 6.0 PEI 2747 0.31981 33583 4.3 NS 18362 2.31982 44176 5.6 NB 17008 2.21983 111317 14.2 QUE 199417 25.41984 110568 14.1 ONT 269915 34.41985 114174 14.5 MAN 34105 4.31986 101770 13.0 SAS 37549 4.81987 106229 13.5 ALB 93992 12.01988 110312 14.0 BC 95185 12.1

YUK 1626 0.2NWT 2044 0.3

inclusive}99.75% of the sample fell in this group.6 These restrictions,combined with a list-wise deletion of observations containing missingvalues or obvious coding errors, resulted in a usable sample of 8156observations. Descriptive statistics for the variables used are given in Table3. A summary of mnemonics and sources of variables not available on themain CMHC database are given in the Appendix.

5. ECONOMETRIC RESULTS

The econometric estimates of the reduced form coefficients, along withsome additional descriptive statistics are presented in Table 4.7 The

Žexplanatory power of each equation as measured by the percentage ofobservations correctly predicted, derived from the conditional estimated

.probabilities is reasonable. If the model were estimated solely withconstants, 37.4% and 68.4% would be correctly predicted for the term andamortization choices, respectively. The improvement of approximately 10and 3 percentage points is typical of microdata, and the significance of theexplanatory variables is confirmed using the likelihood ratio test.

6 Six month mortgages were not generally available during this period. The majority offinancial institutions offered simply the integer choices of 1 to 5 year terms.

7 Ž .While the correlation coefficient r between the reduced form disturbances was notsignificantly different from zero, this does not imply that the structural disturbances wereuncorrelated, and it is not possible to ascertain this from a reduced form model. However, inan earlier version of this paper, we imposed some identifying restrictions and estimated thesystem of structural equations. Evidence of simultaneity in term and amortization choice was

Ž . Ž .indicated by the significance of g and g in Eqs. 10 and 12 , as well as the significant1 2correlation between e and e .1 2


TABLE 3Summary Description of Variables

Variable Mean Std. Dev.

Ž .Term yrs. 3.06 1.62Ž .Amortization yrs. 22.79 3.91

Ž .Age yrs. 32.99 8.56Ž .Married % 67.07 47.00Ž .Nuclear % 73.19 44.30Ž .Children % 47.74 50.00

Ž .Nonspouse dependent % 2.26 14.85Ž .Gross debt service:Income % 22.61 5.64

Ž .Percent loan % 84.41 8.89Ž . Ž .Real 1981 family income $000 32.24 15.61Ž . Ž .Real 1981 house price $000 67.32 18.35

Spread 1.11 0.07Ž .Inflation % 6.53 3.19

Ž .Expectation % 0.44 4.23Ž .5 yr. interest rate % 13.53 2.53

5.1. Demographic Variables

First, demographic influences enter through the age variable. Relative tothe youngest age group, we observe that shorter terms are associated witholder borrowers, with no effects for the very oldest group. Under Type IIbehavior, a short term will be chosen to reduce costs, while a long termwill reduce the risk of rate increases. The consequence of a rate increasebecomes more severe as the payment constraints become more binding.Older borrowers}in particular those aged 50]65}tend to have lowerLTV and GDSY ratios, and thus their financial constraints are less binding.Hence, in contrast to younger households, older households can afford totake a greater risk and reduce the cost of a mortgage by selecting shorterterms. On the other hand, we find no such pronounced relationshipbetween age and amortization.

Second, while we expected that our family structure variable NUCLEARto be important, it did not in fact turn out to be statistically significant ineither equation. The sign however was consistent with our priors: borrow-ers with family responsibilities are more risk averse and take longer termmortgages.8

8 It should be noted that the NUCLEAR and AGE variables are correlated, in that mostnuclear families fall in the young and mid-age groups.


TABLE 4Reduced Form Estimation

Term Amortization

Ž . Ž .NUCLEAR 0.0533 1.84 y0.0195 0.57Ž . Ž .AGE-2 y0.0717 2.51 y0.1021 2.99Ž . Ž .AGE-3 y0.1843 4.53 0.1026 2.09Ž . Ž .AGE-4 y0.2289 3.83 0.1005 1.34Ž . Ž .AGE-5 y0.7198 4.40 0.0912 0.44Ž . Ž .AGE-6 y0.1761 0.66 y0.2382 0.86Ž . Ž .DEL5 3.5123 11.16 1.6436 4.22Ž . Ž .INT5 y0.1718 20.59 y0.0790 8.01Ž . Ž .SPREAD y0.2336 11.25 y0.1682 6.71Ž . Ž .LRINC y0.0038 0.11 0.0732 1.78Ž . Ž .LRPH 0.8009 9.99 1.1657 11.37Ž . Ž .TREND y0.0112 17.11 y0.0077 8.84Ž . Ž .RGN- 2 y0.6774 12.43 0.1673 2.66Ž . Ž .RGN-3 y0.3151 5.02 0.6027 8.07Ž . Ž .RGN-4 y0.6118 10.60 0.5629 8.44Ž . Ž .RGN-5 y0.9797 13.34 0.3676 4.14Ž . Ž .SSN-4 y0.1150 3.66 y0.0187 0.48

Ž . Ž .a 0.7324 1.39 y6.0236 8.981Ž .a 1.8172 3.452

Ž .r y0.0256 1.47

N 8156LLF 12811.82% correct 47.56 71.70

Note: t statistic in parenthesis. Mnemonics are given in the Appendix.

5.2. Market Financial Variables

The interest rate on 5 year mortgages, INT5, has a strongly significantnegative effect on term: higher interest rates reduce the term, and therebyreduce payments. The SPREAD variable indicates similar behavior: thelarger the spread the shorter the term. Since the term structure typicallyhas a positive slope, a large spread implies that long rates are relativelyexpensive compared to short rates and, consequently, the cost of a longerterm is relatively greater, for any interest rate level. We note the SPREADmay also be interpreted as a measure of expectations regarding futurerates since it picks up two points on the yield curve. Sa-Aadu and Sirmansw x15 interpret it in this manner. They also find that it has strong negativeeffects on the term decision.


INT5 and SPREAD also have strongly significant and negative effects onthe choice of amortization. This result is in contrast with much of theaccepted wisdom on mortgage borrowing. It indicates that most borrowersare not so heavily income constrained that they are forced to increase theiramortization length in response to higher interest rates. Rather, theincreased lifecycle costs implied by higher rates can be offset by reducingthe amortization period. A strong indication of this behavior is given inTable 1: amortizations were shortest for 1982, the highest interest rateyear in the sample.9

Type I behavior would predict that, faced with interest rates of 20% andcorrespondingly high monthly payments, individuals may be expected torespond by taking longer, not shorter amortizations. The cost of longamortizations is presented in Table 5; it shows the present discountedvalue of monthly payments on a $100,000 loan for mortgage rates of 10%and of 20%, evaluated for both an 18 year and a 25 year amortization. Fora given personal discount rate, the difference in discounted lifetime costsbetween a 25 and 18 year mortgage increases with the mortgage rate. Forexample, at a personal discount rate of 5%, there is a lifetime mortgagecost differential of $13,224 at a 10% mortgage rate, and of $43,183 at a20% rate. In addition, the percentage increase in monthly paymentsnecessary to take a short amortization is over 10% when interest rates arelow, but only about 2.5% when the rates are high. Faced with thesedifferentials, it is not surprising that a large percentage of borrowers do

TABLE 5Mortgage Schedule for a Loan of $100,000

AmortizationMortgage Discountrate rate 18 year 25 year

10% Monthly payment 999 909

Total mortgage cost 0% 215,966 272,6105% 142,218 155,442

10% 100,000 100,000

20% Monthly payment 1715 1678

Total cost 0% 370,426 503,5365% 243,934 287,116

10% 171,520 184,709

9 We have checked to see if this outcome might be attributable to sample selection, butaverage incomes of borrowers were no higher in 1982 than other years. This indicates that theshorter amortizations were not due to the possibility that it was only higher incomehouseholds who borrowed in that year.


indeed select shorter amortization periods when interest rates are veryhigh.DEL5 captures the effect of expectations. Its significantly positive sign in

the term equation indicates that borrowers tend to lock themselves intolonger terms in the face of rising rates}from a belief that recent trendswill continue. In the amortization equation, DEL5 also has a significantand positive sign; the longer amortization period mitigates the higher costof the longer term.10 We also experimented with longer formation periodsfor expectations with no change in the conclusion regarding their role.

5.3. Indi idual Financial Variables

LRPH has a strongly positive effect on amortization, just as the theorypredicts: higher house prices imply a higher LTV ratio and the resultingbigger mortgage is amortized over a longer period, ceteris paribus. It alsohas a strong positive influence on the term choice. Theoretically, houseprices can have either a positive or negative effect on term. Higher pricesboth increase the cost of a longer term, but expose the borrower to greaterrisk when a shorter term is chosen. The positive coefficient indicates thatthe risk aversion effect appears to dominate.

Ž .The real income efficient LRINC is positive, but only marginallysignificant, in the amortization equation, and not significant in the term

w xequation. Sa-Aadu and Sirmans 15 also failed to find any stronglydeterministic role for income in the mortgage decision. The implication ofthe finding is that the primary influence of income in the housing marketmust be upon the purchase decision rather than upon the type of mortgagechosen. Thus, even though these households are all required to purchaseinsurance, they appear not to stretch themselves unduly in the mortgagepayments decision by purchasing a house which would involve a very high

� 4GDSY ratio; as reported above, only 9% fell in the GDSY bracket 30]35% .

5.4. Other Variables

The fourth set of variables is made up of the regional and seasonalŽ .dummies RGN and SSN, respectively and TREND. In both the term and

the amortization equations, a significant difference between regions isapparent. Relative to region 1, the Atlantic provinces, other regionsportray shorter terms and longer amortization periods. These diverse

10 The model was also estimated without DEL5, since it could be argued that our SPREADvariable is also acting as a proxy for expectations. Interpreted in this way, DEL5 is an adaptivemeasure while SPREAD is a forward looking or rational measure. But only very minimaldifferences in the estimated coefficients emerged, indicating that DEL5 is almost orthogonalto the other variables.


patterns may be attributable to cultural variations and differences in riskw xaversion. Dhillon et al. 6 have also found regional effects.

The seasonal variable in the term equation reflects differences in thenature of dwelling changes at different times of the year. For example,families with school-age children tend to make housing decisions at a timewhich will enable school moves to be made between academic years. Infact, a much smaller percentage of borrowings are made in the finalquarter of the year. Thus families who relocate in the final quarter of the

Ž w x.year may be more mobile than others e.g., Brueckner and Follain 3 , orbe more likely to make unplanned moves}thus choosing shorter mort-gage terms. The coefficients indicate that fourth quarter mortgage appli-cants choose shorter terms than applicants at other times of the year.

The TREND variable indicates that there has been a steady move overtime toward shorter terms and shorter amortizations. The decision toinclude a trend variable was motivated by two factors. First, terms of lessthan 5 years only became available in the late 1970s, and the concept ofsuch short term mortgages may have taken several years before beingwidely accepted. Second, mortgage loan officers believe that borrowershave gradually become more knowledgeable in relation to how interestcosts over the lifecycle of the mortgage vary with interest rates. Thenegative coefficient on the TREND variable is consistent with both of theseinterpretations.

5.5. Policy Simulations

While the results present a coherent picture of mortgage choice, it is ofinterest to examine the effects of policy variables on the probability ofswitching from one term to another or from one amortization to another.We undertake this for two variables, INT5 and SPREAD.

The elasticities are presented in Table 6. The entries in the left-handpanel of the table depict the percentage change in the probability ofchoosing each length of term due to a unit percentage change for each

TABLE 6Elasticities of Term and Amortization Choice with

Respect to Policy Variables

Term Amortization

Short Medium Long Short Long

INT5 2.87 0.18 y2.58 1.25 y0.52SPREAD 0.37 0.02 y0.33 0.25 y0.11


policy variable.11 For example, there is a 2.87% increase in the probabilityof choosing a short term in response to a 1% increase in the 5 year rate,evaluated at the mean of the sample over all mortgage amortizationperiods for the entire sample. Correspondingly, there is a 2.58% fall in theprobability of choosing a long term in response to a 1% increase in the 5year rate. The spread elasticities are interpreted similarly.

The elasticities defining the probability of choosing a short or longamortization period in response to a change in the value of the same twopolicy variables, again evaluated at the sample mean for all term durations,are presented in the right-hand panel. For example, the first entry showsthat there is a 1.25% change in the probability of choosing a shortamortization period in response to a 1% change in the 5 year interest rate.Similar results follow for a change in spread. These simulations indicatethat the term choices in particular are highly elastic with respect tointerest rates, and amortization choice somewhat less so. They thus explainmuch of the variation exhibited in Fig. 1.

6. CONCLUSION

In this paper, we have developed a model of mortgage choice whichinvolves simultaneous decisions on the term and amortization periods byrisk averse, cost minimizing borrowers. We estimated the model using asample of 9000 applicants to the CMHC who were required to takemortgage insurance.

We postulated two possible behavioral models of consumer behavior.The first, which we designated as Type I behavior, occurs when paymentconstraints become strongly binding: that is, the gross debt service to

Ž .income ratio GDSY approaches the maximum permitted level. The sec-ond, designated as Type II behavior, occurs where the monthly paymentconstraint is less binding, and a borrower has the latitude to choose a

Ž . Ž .longer term if risk averse and a shorter amortization if a cost minimizer .A simultaneous reduced form model was estimated containing variablesrelating to demographic, trend, and market and individual financial char-acteristics, as well as to seasonal and regional dummies. Most of thesevariables were found to be strongly significant. To a large extent, thestrength of our results is a function of the quality of the database, as wellas the limited number of mortgage choices open to borrowers in theCanadian market. The most important general result is that borrowers aremotivated by a desire to minimize lifecycle costs and to avoid risks, andType II behavior characterizes most borrowers in this market. Type I

11 While the sum of the probability changes is zero, the sum of the elasticities need not bezero.


behavior is simply not compatible with the observed collinear movement ofboth term and amortization during this period.

In a sensitivity analysis, we examine the effect of a change in policyvariables on the probability of switching from one term to another or fromone amortization period to another. We find that both the short and longterm options, and the amortization period option are responsive to interestrate levels. A policy implication is that interest rate changes lead to largeswings in both term and amortization choices.

APPENDIX: MNEMONICS USED

Ž .Demographic AGE-1 Age - 30 reference category

AGE-2 Age 30]39

AGE-3 Age 40]49

AGE-4 Age 50]59

AGE-5 Age 60]65

AGE-6 Age ) 65

NUCLEAR Unity if married andror children, and no dependent

Financial DEL5 Monthly growth rate of 5 year commercial bank mortgagerate

Ž .Market INT5 Five year commercial bank mortgage rate, average overbanks

SPREAD Ratio of 5 year to 1 year commercial bank mortgage rate

Financial LGDS Natural logarithm of gross debt shelter to income ratio

Ž .Individual LRPH Natural logarithm of real price of housing

Ž .Other RGN-1 Region, Atlantic Provinces reference category

RGN-2 Region, Quebec

RGN-3 Region, Ontario

RGN-4 Region, Prairie Provinces

RGN-5 Region, British Columbia

SSN-4 Season, 4th quarter

TREND Time trend

Endogenous TERM-1 Term s 1 year

TERM-2 Term ) 1 year and - 5 years

TERM-3 Term s 5 years

AMORT-1 Amortization - 25 years

AMORT-2 Amortization G 25 years

Note. Data sources: Applicant specific data: CMHC data base. Commercial bank mort-gage rate: CANSIM vectors B 14050-1. Consumer price index: CANSIM vector D 484000.Regional house price index: Canadian Real Estate Association.


The CANSIM database is maintained by Statistics Canada. Using thisdata, each observation was assigned the 1 year and 5 year averagemortgage rate, based on the individual’s application date. Similarly, theaverage 1 and 5 year rates for the preceding month were also assigned toeach observation, as was the rate of inflation, evaluated as the rate ofchange of CPI over the preceding month. The average rate of inflation was6.5%, with a range of 3.4 to 12.9%. The real 5 year interest rate was 6.9%,with a range of 2.8 to 11%.

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Documents

Instrument Choice: The Demand for Mortgages in Canada