2.1 The Canadian home income plan

Canadians have access to reverse mortgage products through the Canadian Home Income Plan (CHIP) offered by HomeEquity Bank. This program was first offered in the Vancouver area in 1986, and then in Ontario and Alberta starting in 2001. In the following years, the program was gradually offered across the country. In order to be eligible to the program, the borrower must be a Canadian citizen and at least 55 years old. In addition, he or she must be the owner of their own residence. Only primary residences are eligible. The initial loan must be at least $25,000.

The program allows the borrower to remain the owner of the residence, as long as certain conditions are met. These conditions are that the residence must be kept in good condition, property taxes paid, and the property must be insured. Eligibility is dependent on a good record in terms of mortgage re-payment. If there is an existing mortgage on the property at the time of initiation, the mortgage must be paid off first with the proceeds from the reverse mortgage.

The CHIP program provides a NNEG, which means that it guarantees that the amount to be repaid will never exceed the fair market value of the property at the time of sale. Once a loan-to-value limit for the reverse mortgage has been set, the homeowner has several options to choose from in order to receive the funds. They can receive 100% of the funds allowed in one lump sum. They can also initially receive a fraction of the funds granted, in the form of an initial lump sum of $25,000, with subsequent advances. This line of credit option is similar to the Home Equity Conversion Mortgage (HECM) offered in the United States.

There are administrative fees charged to the borrower. First, CHIP charges a closing and administrative fee of $1,495, which includes security lookup, title insurance, and registration. Fees ranging from $175 to $400 are added for an assessment of the property. Finally, a fee between $300 and $500 is charged for independent legal advice.

In 2017, year when we ran our survey and experiment, the CHIP program allowed the borrower to borrow between 10% and 55% of the estimated equity of the residence. Most conditions have not changed since then. The loan-to-value depends on the borrower’s age, sex, and marital status. It also depends on the type of residence and its geographical location. Table 1 provides an example of loan-to-value limits for a single-family dwelling by a single woman between 55 and 75 years old, in the cities of Montreal, Toronto, and Vancouver, in 2017.

Table 1. CHIP maximum loan-to-value: This table presents the maximum loan-to-value ratios of the home equity that can be borrowed by a single woman living in a single-family dwelling. These limits are reported by age and city. Source: HomeEquity Bank, 2017

In order to reduce the losses related to the NNEG, the loan-to-value is lower for younger borrowers. It is also lower for women, since they have a higher life expectancy than men. When compared with single individuals, couples can borrow less since the joint probability of survival is taken into consideration. Finally, according to the type of dwelling and its location, a higher loan is allowed for those for which a higher price growth and a lower price volatility are expected. These reverse mortgages were offered at an interest rate of 5.59% (in 2017) which is above the rate charged on HELOC (4% at the time). Contrary to the United States, these reverse mortgages are not federally insured. ^{Footnote 3}

2.2 The value of reverse mortgages

How should households evaluate reverse mortgages? Their value derives from two distinct sources. The first one is the possibility of shifting consumption earlier when an illiquid asset cannot be sold earlier. This first component is not unique to reverse mortgages. One can also shift consumption earlier by extracting home equity using HELOCs. The second source, which is unique to reverse mortgages, is the insurance against the downside risk that the value of the house falls below the value of the loan at the time the house is sold. Hence, a household may be willing to pay a premium on the interest rate charged for a reverse mortgage due to the NNEG.

The impact of illiquid housing wealth on the desire to borrow from home equity was first studied by Artle and Varaiya (Reference Artle and Varaiya1978). Consumers may value borrowing from home equity in retirement because they are liquidity-constrained. The presence of this illiquid asset endogenously creates these constraints. Consider a household deriving a utility flow from living in their home. While healthy, the household wants to stay in their home. The house value could be expected to appreciate in retirement. Assume the house will only be sold near death, potentially when sickness occurs. These are states of the world where the marginal utility of consumption could be low, in particular in Canada where out-of-pocket medical expenditures in the case of sickness (nursing homes) are not as large as in other countries, such as the United States (Boyer et al. Reference Boyer, De Donder, Fluet, Leroux and Michaud2020). If that is true, the consumption smoothing motive could be strong and push households to extract home equity earlier in retirement, while the marginal utility of consumption is higher. This is the consumption smoothing motive for borrowing against home equity. This should be relevant for those with low levels of liquid assets (relative to income) and with substantial home equity or home equity which is expected to growth fast in retirement.

The second source of value from reverse mortgages is the NNEG. Borrowing a substantial portion of home equity in a HELOC would be risky for the household and their heirs. Since house prices fluctuate substantially, in particular at longer horizons, the loan value at the time the house is disposed off could be larger than the value of the house. Either the consumer or his/her heirs would be liable to repay the financial institution who granted a HELOC. A reverse mortgages allows to transfer this risk to the financial institution offering the loan. Hence, from the point of view of the financial institution, a reverse mortgage is more risky than a regular HELOC, since it cannot recuperate some portion of the loan if house prices fall substantially. Therefore, a mortgage insurance premium must be charged to cover the losses associated with this risk. The actuarial value of the NNEG is a function of various risks including longevity risk and house prices. The higher the likelihood that someone lives longer in their house, the higher the likelihood that the value of their loan exceeds the value of their house. Similarly, drops in house prices increase the likelihood that loans exceed the value of house. Hence, someone who expects house prices to decline, or appreciate more slowly, should perceive a higher value from a reverse mortgage over a HELOC. With growing degree of sophistication in the modeling of risks, there is a substantial literature which evaluate the NNEG for various reverse mortgage products (Li et al. Reference Li, Hardy and Tan2010; Cho et al. Reference Cho, Hanewald and Sherris2015; Alai et al. Reference Alai, Chen, Cho, Hanewald and Sherris2014; Shao et al. Reference Shao, Hanewald and Sherris2015). Davidoff (Reference Davidoff2015) estimates that the value of the NNEG embodied in products offered in the United States can be large, in particular when idiosyncratic house price risk is taken into account. Hence, the value of the NNEG could be nontrivial.

Both motives for borrowing out of home equity suggest a different relationship between the value of reverse mortgages and expected house price growth. They also suggest that the value of reverse mortgages should vary according to a number of other characteristics of borrowers. Putting the two motives together, there has few been attempts to evaluate the value of reverse mortgages to households using a well-defined life cycle framework. For example, Nakajima and Telyukova (Reference Nakajima and Telyukova2017) estimates using a life cycle model that the value of a reverse mortgage to households in the United States is relatively modest, at 252$ per homeowners and 1770$ per reverse mortgage borrower. They attribute this low demand to bequest motive, uncertainty about health, and high cost. Cocco and Lopes (Reference Cocco and Lopes2019) also estimate relatively low value of existing products which they attribute to the requirement of having to maintain the house when contracting a reverse mortgage and to other design features of the product. There is substantial uncertainty around the value of reverse mortgages to retirees.

3.1 The survey

In 2017, we conducted a survey experiment with Asking Canadians, an online panel provider in Canada. Respondents were aged 55 to 75 years and lived in the provinces of Quebec, Ontario, or British Columbia. In each province, 50% of respondents came from major census metropolitan areas (CMA), while the rest came from outside the CMA. We focus on those aged 55 to 75 years because this is an age group where reverse mortgages are likely to be most relevant. Because the value of reverse mortgages is tightly linked to house prices, we focus on provinces in which house price growth has been steady over the last decades. This increases the likelihood that respondents have substantial home equity.

The questionnaire consists of five parts. First, we collect socioeconomic, demographic, and health information from respondents. The second section is on preferences, risk perception, and expectations for the future. The third section measures respondents’ level of financial literacy and knowledge of probabilities. A fourth section asks respondents about their general knowledge about reverse mortgages. Finally, the last section consists of a stated-choice experiment, where respondents were offered different reverse-mortgage products and had to evaluate them by giving their probability of buying each of these financial products within the next year. A copy of the questionnaire can be found in the Online Appendix. ^{Footnote 4} Because the resulting sample is slightly more educated than the general population, we created a set of weights based on the Canadian Community Health Survey (CCHS) for the year 2010. We construct weights based on age group (5 years), gender, province, and education (three levels).

Of the 3,000 Canadians surveyed, 2,399 reported owning a home. A total of 2,306 respondents had enough home equity to borrow from a reverse mortgage. Of these respondents, 2,163 were single or had a spouse aged 55 years or older, making them eligible for the CHIP program. Finally, 2,140 respondents did not have any missing information and therefore were included in the analysis. Descriptive statistics on those respondents is reported in Table 2.

Table 2. Descriptive Statistics: This table presents descriptive statistics on the respondents from the survey. N = 2140. Statistics weighted according to 2010 Canadian Community Health Survey (CCHS)

Respondents are 63.4 years old on average, and half of them are male. Around 20% of them are from British Columbia, 30% from Quebec and 50% from Ontario. Nearly three-quarters (75.5%) of them are married or in a common-law relationship and 76.5% reported having at least one living child. Close to two-thirds (66%) of respondents consider themselves retired. More than half (56.1%) of the sample have an employer pension plan or receive income from one. On average, their annual household income is $88,544, and they have average total non-housing savings of $265,681. ^{Footnote 5} The average current market value of their home is $570,049. Slightly more than a third of respondents (34.1%) still have a mortgage on their primary residence. The median equity value of their residence is around $520,000. To define a group who is house-rich and cash-poor, we borrow from the definition of wealthy hand-to-mouth households proposed by Kaplan et al. (Reference Kaplan, Violante and Weidner2014). They define wealthy hand-to-mouth consumers as those with positive home equity but liquid assets less than half of total income. To capture the house-rich aspect of the definition we are after, we tighten the criterion on home equity and use a threshold of three times total income instead of zero home equity. Respondents who have home equity larger than three times their income but liquid assets (savings) less than half their total income are defined as house-rich and cash-poor. In the sample, 9.2% of respondents qualify as house-rich and cash-poor.

In terms of preferences, we keep two variables for our analysis: one which is a proxy for the presence of a bequest motive and the other to proxy attachment to the house. On a 5-point Likert scale, respondents were asked if they agreed with the following statement: Parents should set aside money to leave to their children or heirs once they die, even when it means somewhat sacrificing their own comfort in retirement. We recoded those who agree or strongly agree have shown preferences consistent with a bequest motive (or bequest norm). In the sample, 17.8% of respondents were classified using this statement as having a stronger bequest motive. We also use the response to the statement: A house is an asset that should only be sold in the case of financial hardship to characterize a respondent’s preference or norm for staying in the home. In the sample, 44% agreed or strongly agreed with the statement.

We asked respondents a series of three questions to assess their level of financial literacy following Lusardi and Mitchelli (Reference Lusardi and Mitchelli2007). The first question is on interest rates, the second on purchasing power, and the third on risk diversification. We create a binary indicator taking value 1 if the respondent correctly answers all three questions and 0 if not. Overall, 54.1% of respondents correctly answer all three questions. Another question asks the respondent about survival probabilities. Respondents are told the probability of surviving to 85 is 60% and asked whether the probability of surviving to 60 is larger, or smaller than 60%. We create a binary indicator if the respondent correctly answers this question. 84.6% of respondents correctly answered this question.

3.2 Prior knowledge of RMR

Respondents were asked a sequence of questions with the objective of measuring their level of prior knowledge of reverse mortgages.

Without naming the financial product, we first presented a sentence containing the definition of a reverse mortgage to the respondents ^{Footnote 6} . Then, respondents were asked if they had ever heard of this financial product. As shown in Table 3, 77.3% of eligible Canadian homeowners claimed to have heard of that kind of financial product. Fewer homeowners from Quebec answered having heard this definition, a difference of nearly 20 percentage points with the two other provinces.

Table 3. Prior knowledge of reverse mortgages: N = 2140. Statistics weighted according to the 2010 Canadian Community Health Survey (CCHS)

Then, we asked those who claimed to have heard of this financial product if they could name it. 59.5% of these homeowners claimed to be able to name the product in question. Once again, there was a noticeable difference between provinces. Fewer homeowners from Quebec who had heard of this financial product claimed to be able to name it, a difference of 15 percentage points with the two other provinces.

Finally, those who claimed to be able to name the product were asked to identify it from a list of financial product names. 96.8% of them answered correctly. Once again, fewer homeowners from Quebec answered this question correctly. Overall, 44.52% of all homeowners had heard of the existence and correctly identified the reverse mortgage as the name of that financial product. Moreover, the level of knowledge was twice as big among homeowners in Ontario and British Columbia than it was in homeowners in Quebec. One plausible explanation for this phenomenon is that the CHIP program has been offered longer in Ontario and British Columbia than in the province of Quebec.

To understand how prior knowledge of the product is distributed, we estimate a logit regression with as a dependent variable an indicator for whether or not respondents were able to identify the product (answer all three questions and named the product correctly as a reverse mortgage). We include as controls an indicator for financial literacy, for understanding survival probabilities, sociodemographic characteristics, and controls for economic resources. In Table 4, we report estimates of marginal effects along with standard errors.

Table 4. Who can identify reverse mortgages?: Marginal effects from a logit regression of whether or not respondents understand reverse mortgages (could identify by name based on description) on a series of controls. Total wealth, home value, and savings are included as quartile dummies and the 4th quartile is excluded

Standard errors in parentheses

*** p<0.01, ** p<0.05, * p<0.1

We find that those with higher levels of financial literacy have a substantially higher probability of knowing what a reverse mortgage is. Even after controlling for a host of factors, there is a 12.2 percentage point difference in knowledge of reverse mortgages between those with and those without financial literacy. There is also a substantial difference between those who understand of survival probabilities and those who don’t. In terms of other correlates, males are more likely to know reverse mortgages. Those with kids are less likely to know about reverse mortgages. In terms of income, those with the lowest level of income (bottom quartile) are less likely to know about reverse mortgages. Those in the second and third quartile of home equity are more likely to know about reverse mortgages (these effects are relative to the fourth quartile). Quite the opposite, those in lowest quartiles of liquid savings are less likely to know about reverse mortgages. Respondents with existing mortgages are more likely to know about reverse mortgages. Interestingly, we do not find that those who are house-rich and cash-poor are more likely to know about the existence of reverse mortgages. In terms of economic resources, those who appear to know about reverse mortgages do not exactly fit the profile of house-rich and cash-poor households. However, they are more financially literate.

4.1 Computing the actuarial value of the NNEG

To compute the actuarial value of each of the contracts offered to respondents, we consider a simple pricing framework. Reverse mortgage pricing models can be extremely sophisticated and account for a number of elements, including stochastic discount factors, yield curve modeling, and endogenous termination probabilities (see e.g., Shao et al. Reference Shao, Hanewald and Sherris2015). Since we are interested in the cross-sectional and cross-scenario variation in the actuarial value of the contracts we presented, we will pay more attention to the variation induced across respondents and scenarios than the absolute level of the actuarial value of the NNEG in terms of a mortgage insurance premium. Another important distinction with other pricing models is that we aim to measure the perceived value of the NNEG rather than the actual NNEG. Hence, we will use subjective mortality risk instead of life table risk.

We compute fair mortgage insurance premiums to cover losses related to the NNEG. Let ${\gamma _{i,j}}$ be the loan-to-value ratio of the equity of the house with (net equity) value ${H_{i,a}}$ , borrowed by an individual i of age a in scenario j. The initial value of the loan, ${L_{a,i,j}}$ , is then given by ${L_{a,i,j}} = {\gamma _{i,j}}{H_{i,a}}$ . The value of the loan at $a + t$ is given by:

(1) $${L_{a + t,i,j}} = {L_{a,i,j}}{(1 + {r_{LC}} + {\pi _{i,j}})^t},$$

where ${r_{LC}}$ represents the (fixed) interest rate for a HELOC, ${\pi _{i,j}}$ represents a fair mortgage insurance premium to cover losses related to the NNEG in scenario j, and let $r_{i,j}^* = {r_{LC}} + {\pi _{i,j}}$ represents the (fair) interest rate for the reverse mortgage. Let ${H_{i,a + t}}$ be the resale value of the house if the borrower leaves or dies after t years (at age $a + t$ ). The NNEG ensures that the amount recovered by the lender at the time of the sale of the house is

(2) $$\min \{ {L_{a + t,i,j}},(1 - c){H_{i,a + t}}\} ,$$

where c is a transaction cost calibrated at 5% of the selling price ^{Footnote 11} of the selling price. The potential loss by the lender at the time of selling the house is then defined as:

(3) $$\max \{ {L_{a + t,i,j}} - (1 - c){H_{i,a + t}},0\} .$$

The expected present value of future losses related to the NNEG is given by:

(4) $${\rm{NNEG}}({\pi _{i,j}}) = {E_H}\left( {\sum\limits_{t = 1}^T {q_{i,a,a + t}}{{max({L_{a + t,i,j}} - (1 - c){H_{i,a + t}},0)} \over {{{(1 + i)}^t}}}} \right),$$

where i is a discount rate-based calibrated to 4% and ${q_{i,a,a + t}}$ is the conditional probability of dying at age $a + t$ for someone of age a at $t = 0$ . These probabilities are respondent-specific. Finally, ${E_H}$ is the expectation operator for the distribution of future house prices which depends on the region of the country and the type of dwelling. For the lender, the expected present value of the accumulated mortgage insurance premiums paid is given by:

(5) $${\rm{MIP}}({\pi _{i,j}}) = {\pi _{i,j}}{E_H}\left( {\sum\limits_{t = 1}^T {s_{i,a,a + t}}{{{L_{a + t,i,j}}} \over {{{(1 + i)}^t}}}} \right),$$

where ${s_{i,a,a + t}}$ is the conditional probability to survive at age $a + t$ for someone aged a at $t = 0$ . Finally, the actuarial fair mortgage insurance premium ${\pi _{i,j}}$ is such as:

(6) $${\rm{NNEG}}({\pi _{i,j}}) = {\rm{MIP}}({\pi _{i,j}}).$$

The mortgage insurance premium ${\pi _{i,j}}$ is the actuarial value of the NNEG guarantee for the risk profile of the respondent. The fair rate on the reverse mortgage is $r_{i,j}^* = {r_{LC}} + {\pi _{i,j}}$ . To compute the value of the NNEG for each respondent and scenario, we need estimates of house price dynamics as well as survival probabilities.

We first set the interest rate of a HELOC ${r_{LC}}$ at 4%, which is the average rate that was offered on the Canadian market in 2017 ^{Footnote 12} . We set the maximum loan-to-values offered by CHIP as reported in Table 1 but use the loan-to-value offered in each scenario using the randomization. We also use a constant discount rate of 4% (i) in the computations.

4.1.1 House price dynamics

We calibrate house price dynamics using the MLS Home Price Index from the Canadian Real Estate Association (CREA), which provides information on housing prices in the major CMAs in Canada. This data set provides information regarding the average price of all types of dwellings, as well as the average price per type of dwelling, namely single-family dwellings, townhouses, and condos. We used monthly data from January 2005 to August 2016 for the cities of Vancouver, Toronto, and Montreal. Figure 1 presents the evolution of the composite price index between 2005 and 2018 for all of Canada, as well as for the cities of Vancouver, Toronto, and Montreal. We see that Vancouver and Toronto are the cities that have had the most substantial growth, with an average annual growth of 6% and 6.8%, respectively, while the city of Montreal experienced an average annual growth of 3.7%. The cities of Vancouver and Toronto also demonstrate having higher variability in prices when compared to the city of Montreal. We drop the last 2 years (2017 and 2018) since the survey was conducted in 2017.

Figure 1. MLS Home Price Index for the cities of Vancouver, Toronto, and Montreal, from 2005 to 2018

We estimate parameters of the house price dynamic using an AR(1) with a deterministic trend:

(7) $$\log {H_{h,p,m}} = \delta_{h,p}\ {m+\epsilon_{h,p,m}}$$

(8) $${\epsilon_{h,p,m}} = \rho_{h,p}\epsilon_{h,p,m-1}+\eta_{h,p,m},$$

where H_h,p,m is the average house price of type h, in the city p in the month m, ${\delta _{h,p}}$ is the deterministic trend, and ${\eta _{h,p,m}}$ is an idiosyncratic error term which is assumed normally distributed with an average of zero and a variance of $\sigma _{h,p}^2$ . Table 5 reports estimates by type of dwelling for the cities of Vancouver, Toronto, and Montreal. In each specification, the coefficient of the deterministic trend and the autocorrelation coefficient are significant at a level of 1%. House prices exhibit behavior similar to a random walk with some degree of mean-reversion. These estimates were used to calibrate the house price risk in the provinces of Quebec (Montreal), Ontario (Toronto), and British Columbia (Vancouver). While the dynamics in house prices evolve at the monthly level, they are aggregated in simulations at the annual level (when survival and other outcomes are computed).

Table 5. House price dynamic estimates: This table reports estimated parameters of the house price dynamics by city and type of dwelling. SFD refers to a single-family dwelling. ${\delta _{h,p}}$ is the monthly deterministic trend, ${\rho _{{h_p}}}$ is the AR(1) coefficient, and ${\sigma _{h,p}}$ is the standard deviation of shocks for a dwelling of type h and in city p. SFD refers to single-family dwelling. * $p \lt 0.1$ , ** $p \lt 0.05$ , *** $p \lt 0.01$

Using an aggregate house price index to estimate the dispersion of shocks, as we did, underestimates the volatility in selling prices, since an important component of the volatility in house prices is house-specific and likely idiosyncratic (Davidoff Reference Davidoff2015). Since we do not have Canadian information on the dispersion of house prices within CMA, we instead resort to scaling up the standard deviation of shocks. Nakajima and Telyukova (Reference Nakajima and Telyukova2017) estimate using zip-code-level data a process which is similar to ours (AR(1)). They find an annual standard deviation of (log) house price shocks of 0.125. Our estimates, which vary by CMA and dwelling, are of the order of 0.06 at the annual level. Hence, we scale up the standard deviation of the shocks by a factor of 2 for our computations.

Respondents likely form their own expectations about house price growth. What do respondents expect about house price growth in years following the experiment? We asked respondents to categorize their expectation of their house’s price growth over the next 5 years: more than 20%, between 5% and 20%, between −5% and 5%, between −20% and −5%, and less than −20%. Table 6 reports the distribution of subjective expectations for house price growth over the next 5 years by province. Homeowners from the province of British Columbia are those who expected a higher growth, with almost 80% of them expecting a growth higher than 5%. Homeowners from Ontario and Quebec followed, with 75% and 66% expected growth higher than 5%. If we use the expected growth rates in Table 5, we obtain a 5-year expected growth rate for 43% in British Columbia for single-family dwellings and 27% for other types of dwellings. Expected 5-year growth rates are in excess of 35% in Ontario, while they are around 20% for Quebec. This suggests that a significant fraction of respondents were more pessimistic than historical house price growth at the time of the survey, in particular for British Columbia and Ontario. While there is no direct way to incorporate these expectations in the calculation of the NNEG, we will assess the role of these expectations in shaping demand for reverse mortgages.

Table 6. Subjective expectation of house price growth over the next 5 years: This table presents the distribution of subjective expectation of house price growth over the next 5 years by province (N=2140). Statistics weighted according to the 2010 Canadian Community Health Survey (CCHS)

4.1.2 Survival rates

Since respondents are likely to evaluate the NNEG using their own beliefs about survival, we exploit a question on subjective survival beliefs which has been shown to be predictive of actual mortality (Hurd and McGarry Reference Hurd and McGarry2002). We asked respondents to provide us with the probability they will live up to the age of 85 years. To transform this into a life table, we use the structure of official life table survival risk by age and adjust those using the information in the subjective beliefs. We follow the approach used by Salm (Reference Salm2010) to model deviations from life table survival. Assume the subjective mortality hazard of respondent i at age a be given by:

(9) $$\lambda _a^S({x_i}) = {\psi _i}\lambda _a^O({x_i}),$$

where $\lambda _a^O({x_i})$ is the individual’s objective mortality hazard based on life tables ( ${x_i}$ correspondents to province, sex and cohort). In the survey, each respondent was asked to give his subjective probability of surviving until the age of 85 years, $s_{a,85}^S({x_i})$ . We use this information to estimate ${\psi _i}$ . Appendix A provides details on how we estimate this parameter. To avoid indeterminate values at the bounds, we set $s_{a,85}^S({x_i}) = 0.01$ as a minimum and $s_{a,85}^S({x_i}) = 0.99$ as a maximum for subjective risk responses. Based on the objective life table of individual i, it is then possible to use ${\psi _i}$ and reconstruct their subjective life table using equation 9.

Table 7 reports the distribution of remaining years of life among respondents by age groups in the sample. It also reports the average remaining years of life according to the official life tables. On average, the expected number of remaining years of life is 23.4 years using the prospective life tables from Statistics Canada and 29 years using the subjective probabilities. Hence, our respondents overestimate survival to the age of 85 years. ^{Footnote 13} There is also considerable dispersion in subjective remaining life expectancy with the 25th percentile at the age of 65–69 years expecting to live fewer than 14.8 years on average while the same number is 29.8, nearly double, at the 75th percentile.

Table 7. Expected remaining years of life: This table reports statistics for subjective and life table remaining life expectancy (N=2140). Statistics weighted according to the 2010 Canadian Community Health Survey (CCHS)

4.2 Estimates of the actuarial value of the NNEG

For each respondent, we first use subjective survival probabilities to generate 1000 draws of death ages which are termination probabilities for the sake of this exercise. For couples, we use the death of the last spouse alive. For spouses, we do not have subjective survival curves. Assuming life table probabilities would lead to an assumption that there is no correlation in life expectancy across spouses. Instead, we use the subjective survival curve of the respondent. Using the age of death as termination age for the reverse mortgage overestimates the duration of reverse mortgage contracts as many respondents are likely to sell their property prior to death. This should lead to an overestimation of the value of the NNEG. We then use the house price process by province and dwelling type of the respondent to generate a distribution of house prices at the time of disposition. Since mortality and house prices are independent, we assume there the decision to sell the house is independent of house prices.

Using the distribution of selling prices and the distribution of durations (time to mortality or termination), we compute both the expected present discounted value of mortgage insurance premiums and NNEG losses for the insurer. We then solve over a grid for the mortgage insurance premium which solves the zero-profit condition. We do this for each of the 2140 respondents and for each 5 scenarios. We express the estimates of ${\pi _{i,j}}$ in basis points (100 basis point is one percentage point).

Figure 2 shows the distribution of actuarial values of the NNEG across respondents and scenarios for two sets of assumption: the baseline scenario using house price growth estimated over the period 2005–2016 and one where annual growth in house prices ( $\delta $ ) is 50% lower. On average, the actuarial value of the NNEG, represented as a premium on the HELOC rate, is 31 basis points, or 0.31 percentage point. It varies substantially across the sample and scenarios with a standard deviation of 39.7, a first quartile of 13 basis points, and a 90th percentile of 86 basis points. Under the alternative scenario with lower growth, the premium is on average higher, with a mean of 77 basis points and a standard deviation of 57, a 90th percentile 155 basis points. Hence, these estimates are well below the observed premium in the market of over 200 basis points. One needs however to be careful with concluding that the observed premium is too high. We focus on house price trends in three major cities with substantial growth. If growth is much lower in rural areas, for example, this could justify higher premiums, as the sensitivity of our premium estimates to house price growth shows.

Figure 2. Actuarial Value of NNEG: Density estimate of the distribution of NNEG mortgage insurance premiums computed across respondents and scenarios (rate in excess of HELOC). The premium is reported in basis points (100 = 1 percentage point). The distribution is reported in blue for the reference scenario (with historical growth in house prices 2005–2016) and with an alternative scenario (in orange) where historical growth is half of what has been observed by dwelling type and province.

To shed light on the variation in the values we computed, we run a regression of the premium in basis point on demographics, subjective remaining life expectancy, and the amount borrowed in terms of Loan-to-Value (LTV) in the scenario. As one would expect due to the effect of mortality on the value of the NNEG, the premium decreases with age (duration lower) and is lower for males and higher for couples. The premium is higher in British Columbia and Ontario. The premium increases with the LTV that is granted as a reverse mortgage in each scenario.

5.1 House price growth expectations

Given the central importance of house price expectations, we first look at the correlation between subjective house price expectations over the next 5 years and the probability of purchasing a reverse mortgage in the scenarios presented. We use the average take-up probability over the five scenarios. If the value of the NNEG is what drives demand for reverse mortgages, we should expect a negative correlation between purchase probabilities and house price growth expectations. On the other hand, if the consumption smoothing motive is more important, we should see a positive correlation between the two outcomes.

Table 8 reports average take-up probabilities by province and house price growth expectations. For both Quebec and Ontario, there is a strong positive gradient between subjective house price growth and take-up probabilities. Those who expect the highest growth are more likely to purchase a reverse mortgage in the scenarios we presented. Hence, this would suggest these respondents are motivated by the possibility of taking advantage now of some of the home equity increase they expect to obtain in the future. It could also mean they poorly understand the value of the NNEG. For British Columbia, we do not observe such a gradient which may be due to the fact that most respondents expected substantial house price growth.

Table 8. Probability of buying a reverse mortgage within the next year: This table presents the average probability of buying a reverse mortgage within the next year by province and category of subjective expectation on the house price growth over the next 5 years (N=2140). Statistics weighted according to the 2010 Canadian Community Health Survey (CCHS)

5.2 Regression analysis

To understand the determinants of take-up probabilities and in particular how respondents respond to the interest rate and the fair value of the NNEG, we specify the following semi-log regression model:

(10) $${p_{i,j}} = {\alpha _r}\log {r_{i,j}} + {\alpha _f}\log r_{i,j}^* + {X_i}\beta + {\varepsilon _{i,j}}.$$

where ${p_{i,j}}$ is the reported take-up probability (in percentage points from 0 to 100), ${r_{i,j}}$ is the interest rate on the reverse mortgage in scenario j, and $r_{i,j}^* = {r_{LC}} + {\pi _{i,j}}$ is the interest rate obtained by adding to the HELOC rate of 4% the fair mortgage insurance premium computed for each respondent and scenario, ${\pi _{i,j}}$ . The vector X_i contains a number of respondent-level characteristics, while ${\varepsilon _{i,j}}$ is an error term. With this specification, the interest rate elasticity of demand is given by ${{{\alpha _r}} \over {\overline p }}$ where $\overline p $ is a fixed level of the take-up probabilities where the elasticity is evaluated (such as the mean).

The specification nests the case where ${\alpha _r} = - {\alpha _f}$ in which case we can express the choice probability as a function of the log of the ratio of the interest rate to the fair rate, a measure of the unfairness of the interest rate charged in the reverse mortgage. Davidoff and Wetzel (Reference Davidoff and Wetzel2014) show that consumers may have a hard time correctly evaluating the value of the NNEG and therefore the fair rate in the reverse mortgage. This would lead to the prediction of an imprecise estimate of ${\alpha _f}$ , potentially different from ${\alpha _r}$ . We can test this assumption given estimation of equation (10).

We control for a rich set of covariates from the survey, including quartiles of income, home value, and savings as well as controls for preferences as well as house price expectations. We estimate parameters by ordinary least square (OLS) using clustered standard errors at the respondent level. ^{Footnote 14}

Table 9 reports OLS coefficients for the full sample as well specifications where we estimate parameters separately by financial literacy as well as a third group representing those who know reverse mortgages and have a high level of financial literacy.

Table 9. Regression estimates: The table reports coefficients estimates from OLS along with (clustered) standard errors in parenthesis. The dependent variable is the take-up probability in percentage points (from 0 to 100). The first column reports estimates on the whole sample. The second and third column report estimates by level of financial literacy. The last column reports results for the subset of those who have high financial literacy and also have prior knowledge of reverse mortgages prior to the experiment. We report below the R-squared the interest rate elasticity computed at the mean in the total sample as well as the standard error. We also report the p-value on the test for the equality of the coefficients on the log interest rate and the log of the fair rate. Statistical significance is denoted using * $p \lt 0.1$ , ** $p \lt 0.05$ , *** $p \lt 0.01$

Robust standard errors in parentheses

*** p<0.01, ** p<0.05, * p<0.1

For the full sample, the estimated interest rate elasticity is −0.823 and statistically significant. This suggest that consumers are quite sensitive to the price of reverse mortgages. In the full sample, they are however insensitive to the fair rate that represents the actuarial value of the mortgage insurance premium that covers the NNEG. The estimate is positive but statistically insignificant. Although we do not reject the equality ${\alpha _r} = - {\alpha _f}$ (p-value = 0.843), this largely reflects the imprecision of ${\alpha _f}$ . Hence, we find respondents have trouble using the NNEG as in Davidoff and Wetzel (Reference Davidoff and Wetzel2014). When we split the sample between those with high financial literacy (who could answer correctly all three questions) and those with low financial literacy, we observe that the interest sensitivity is entirely driven by those with high financial literacy. Among those, the price elasticity is −1.149 (se=0.164), suggesting a relatively high level of price sensitivity while it is −0.318 and statistically insignificant among those with low financial literacy. The difference between the two estimates is statistically significant (t = −2.89). Moreover, those with high financial literacy are more likely to purchase reverse mortgage products with a higher value of the NNEG. A 10% increase in the value of the NNEG increases demand by 1.67 percentage points. Among those with low financial literacy, the coefficient on the (log) value of the NNEG is imprecisely estimated to be negative. Hence, financial literacy appears to help respondents with the evaluation of the NNEG. In the last column, we refine even further the specification to exclude those who have high financial literacy but did not know the product prior to the experiment. Although we obtain an even larger interest rate elasticity (−1.479), we do not detect a higher sensitivity to the value of the NNEG among this group (the estimate is of similar size but more imprecise). Overall, we find that despite the lack of effect of financial literacy on average take-up probabilities, financial literacy appears to help consumers in evaluating the reverse mortgage products presented.

In terms of demographics, some differences in demand are observed. Demand appears to decrease with age and is higher for males in the full sample. The effect of age is concentrated among those with higher financial literacy and knowledge of the product, while gender differences are widespread across groups. In terms of economic resources, there is some indication that those with low savings and low income, in particular among those with higher financial literacy, have higher demand for reverse mortgages (the 4th quartile is omitted for these variables). However, there is no relationship between demand and the house-rich and cash-poor variable indicator. Therefore, there is some evidence that demand is higher among those with lower resources (both income and savings) but not necessarily the specific group of house-rich and cash-poor respondents. We find that those with an existing mortgage are more likely to purchase a reverse mortgage. In this case, they must pay first the existing mortgage with the funds from the reverse mortgage. Purchasing a reverse mortgage for these households may allow to effectively postpone mortgage payments until they sell the house (by clearing the existing mortgage and avoiding payments while living in the house). For house price expectations, we find some evidence that those who expect higher price growth are more likely to purchase a reverse mortgage. Expecting negative growth is negatively correlated with demand for reverse mortgages. However, this relationship is not always statistically significant and monotonic.

Finally, there is some evidence that households who want to stay in their house unless they experience financial hardship are more likely to demand a reverse mortgage. This is consistent with the consumption smoothing motive as those households are less willing to sell their house to finance consumption at older ages. We find that those who think that leaving money to their heirs is important are more likely to purchase a reverse mortgage. While a bequest motive should decrease demand for reverse mortgages, it is possible that these households are inclined to make inter vivos transfers with the proceeds from the reverse mortgage. Overall, several findings are puzzling and one interpretation is that reverse mortgages are poorly understood by respondents, in particular those with lower financial literacy.